modelos estad´ısticos dinámicos para análisis de evolución de

Universidad Politecnica de Madrid

Escuela Tecnica Superior de Ingenieros Industriales

Modelos Estadısticos Dinamicos

para Analisis de Evolucion de

Tasas de Accidentes:

Metodologıa y Herramientas

Computacionales

Tesis Doctoral

BAHAR DADASHOVA

Madrid 2014

Departamento de Ingenierıa Mecanica y Fabricacion

Escuela Tecnica Superior de Ingenieros Industriales

Modelos Estadısticos Dinamicos

para Analisis de Evolucion de

Tasas de Accidentes:

Metodologıa y Herramientas

Computacionales

Tesis Doctoral

BAHAR DADASHOVA

TUTORES:

Blanca Arenas Ramırez Jose Mira McWilliamsDoctor Ingeniero de Caminos, Doctor Ingeniero IndustrialCanales y Puertos

Tribunal nombrado por el Magfco. y Excmo. Sr. Rector de la UniversidadPolitecnica de Madrid, el dıa de diciembre de 2014.

Presidente: D. Francisco Aparicio Izquierdo

Secretario: D. Camino Gonzalez Fernandez

Vocal: D. Emilio Larrode Pellicer

Vocal: D. Juan de Ona Lopez

Vocal: D. Alvaro Gomez Mendez

Suplente: D. Francisco Garcıa Benıtez

Suplente: D. Alberto Lopez Rozado

Realizado el acto de defensa y lectura de la tesis el dıa de diciembre de2014 en la E.T.S. Ingenieros Industriales.

CALIFICACION:

EL PRESIDENTE

LOS VOCALES

EL SECRETARIO

Acknowledgements

I would like to express my sincere gratitude to my supervisors, Blanca Arenasand Jose Mira for all their effort and time and to Francisco Aparicio, for givingme an opportunity to be a part of University Institute of University Instituteof Automobile Research-INSIA. I would like to thank to my family for theirconstant support and understanding, and also take the opportunity to wishmy brother Sabuhi Dadashov best luck in his doctorate studies.

I would also like to thank Rosario Romero, Camino Gonzalez, EdinalvaGomes, Filip Van den Bossche and Frits Bijleveld for their help and col-laborations; and to all of my friends and collegues, particularly, to ArgyroAvgoustaki, Jessica Viqueira, Raquel de Roa, Nasima Akalou, Azadeh Nasiriand Ana Laura Badagian for their invaluable presence along this way.

I gratefully acknowledge the funding sources that made my researchpossible.

iii

Abstract

Road accidents are a very relevant social phenomenon and one of the maincauses of death in industrialized countries. Sophisticated econometric modelsare applied in academic work and by the administrations for a better under-standing of this very complex phenomenon. This thesis is thus devoted to theanalysis of macro models for road accidents with application to the Spanishcase. The objectives of the thesis may be divided in two blocks:

a. To achieve a better understanding of the road accident phenomenon bymeans of the application and comparison of two of the most frequentlyused macro modelings: DRAG (demand for road use, accidents andtheir gravity) and UCM (unobserved components model); the applica-tion was made to van involved accident data in Spain in the period2000-2009. The analysis has been carried out within the frequentistframework and using available state of the art software, TRIO, SASand TRAMO/SEATS.

b. Concern on the application of the models and on the relevant inputvariables to be included in the model has driven the research to tryto improve, by theoretical and practical means, the understanding onmethodological choice and model selection procedures. The theoreticaldevelopments have been applied to fatal accidents during the period2000-2011 and van-involved road accidents in 2000-2009.

This has resulted in the following contributions:

a. Insight on the models has been gained through interpretation of theeffect of the input variables on the response and prediction accuracyof both models. The behavior of van-involved road accidents has beenexplained during this process.

b1. Development of an input variable selection procedure, which is crucialfor an efficient choice of the inputs. Following the results of a) the

v

procedure uses the DRAG-like model. The estimation is carried outwithin the Bayesian framework. The procedure has been applied forthe total road accident data in Spain in the period 2000-2011. Theresults of the model selection procedure are compared and validatedthrough a dynamic regression model given that the original data has astochastic trend.

b2. A methodology for theoretical comparison between the two modelsthrough Monte Carlo simulation, computer experiment design and ANOVA.The models have a different structure and this affects the estimation ofthe effects of the input variables. The comparison is thus carried outin terms of the effect of the input variables on the response, which is ingeneral different, and should be related. Considering the results of thestudy carried out in b1) this study tries to find out how a stochastictime trend will be captured in DRAG model, since there is no specifictrend component in DRAG. Given the results of b1) the findings of thisstudy are crucial in order to see if the estimation of data with stochas-tic component through DRAG will be valid or whether the data need acertain adjustment (typically differencing) prior to the estimation. Themodel comparison methodology was applied to the UCM and DRAGmodels, considering that, as mentioned above, the UCM has a specifictrend term while DRAG does not.

b3. New algorithms were developed for carrying out the methodologicalexercises. For this purpose different softwares, R, WinBUGs and MAT-LAB were used.

These objectives and contributions have been resulted in the followingfindings:

1. The road accident phenomenon has been analyzed by means of twomacro models: The effects of the influential input variables may beestimated through the models, but it has been observed that the esti-mates vary from one model to the other, although prediction accuracyis similar, with a slight superiority of the DRAG methodology.

2. The variable selection methodology provides very practical results, asfar as the explanation of road accidents is concerned. Prediction ac-curacy and interpretability have been improved by means of a moreefficient input variable and model selection procedure.

3. Insight has been gained on the relationship between the estimates ofthe effects using the two models. A very relevant issue here is the roleof trend in both models, relevant recommendations for the analyst haveresulted from here.

The results have provided a very satisfactory insight into both modelingaspects and the understanding of both van-involved and total fatal accidentsbehavior in Spain.

Resumen

Los accidentes del trafico son un fenomeno social muy relevantes y una de lasprincipales causas de mortalidad en los paıses desarrollados. Para entendereste fenomeno complejo se aplican modelos econometricos sofisticados tantoen la literatura academica como por las administraciones publicas. Esta tesisesta dedicada al analisis de modelos macroscopicos para los accidentes deltrafico en Espana.

El objetivo de esta tesis se puede dividir en dos bloques:

a. Obtener una mejor comprension del fenomeno de accidentes de traficomediante la aplicacion y comparacion de dos modelos macroscopicosutilizados frecuentemente en este area: DRAG y UCM, con la apli-cacion a los accidentes con implicacion de furgonetas en Espana du-rante el perıodo 2000-2009. Los analisis se llevaron a cabo con enfoquefrecuencista y mediante los programas TRIO, SAS y TRAMO/SEATS.

b. La aplicacion de modelos y la seleccion de las variables mas relevantes,son temas actuales de investigacion y en esta tesis se ha desarrollado yaplicado una metodologıa que pretende mejorar, mediante herramientasteoricas y practicas, el entendimiento de seleccion y comparacion delos modelos macroscopicos. Se han desarrollado metodologıas tantopara seleccion como para comparacion de modelos. La metodologıa deseleccion de modelos se ha aplicado a los accidentes mortales ocurridosen la red viaria en el perıodo 2000-2011, y la propuesta metodologica decomparacion de modelos macroscopicos se ha aplicado a la frecuenciay la severidad de los accidentes con implicacion de furgonetas en elperıodo 2000-2009.

Como resultado de los desarrollos anteriores se resaltan las siguientes con-tribuciones:

a. Profundizacion de los modelos a traves de interpretacion de las variablesrespuesta y poder de prediccion de los modelos. El conocimiento sobre

ix

el comportamiento de los accidentes con implicacion de furgonetas seha ampliado en este proceso.

b1. Desarrollo de una metodologıa para seleccion de variables relevantespara la explicacion de la ocurrencia de accidentes de trafico. Teniendoen cuenta los resultados de a) la propuesta metodologica se basa enlos modelos DRAG, cuyos parametros se han estimado con enfoquebayesiano y se han aplicado a los datos de accidentes mortales entrelos anos 2000-2011 en Espana. Esta metodologıa novedosa y originalse ha comparado con modelos de regresion dinamica (DR), que sonlos modelos mas comunes para el trabajo con procesos estocasticos.Los resultados son comparables, y con la nueva propuesta se realizauna aportacion metodologica que optimiza el proceso de seleccion demodelos, con escaso coste computacional.

b2. En la tesis se ha disenado una metodologıa de comparacion teorica entrelos modelos competidores mediante la aplicacion conjunta de simulacionMonte Carlo, diseno de experimentos y analisis de la varianza ANOVA.Los modelos competidores tienen diferentes estructuras, que afectan a laestimacion de efectos de las variables explicativas. Teniendo en cuentael estudio desarrollado en b1) este desarrollo tiene el proposito de de-terminar como interpretar la componente de tendencia estocastica queun modelo UCM modela explıcitamente, a traves de un modelo DRAG,que no tiene un metodo especıfico para modelar este elemento. Los re-sultados de este estudio son importantes para ver si la serie necesita serdiferenciada antes de modelar.

b3. Se han desarrollado nuevos algoritmos para realizar los ejercicios metodologicos,implementados en diferentes programas como R, WinBUGS, y MAT-LAB.

El cumplimiento de los objetivos de la tesis a traves de los desarrollos antesenunciados se remarcan en las siguientes conclusiones:

1. El fenomeno de accidentes del trafico se ha analizado mediante dosmodelos macroscopicos. Los efectos de los factores de influencia sondiferentes dependiendo de la metodologıa aplicada. Los resultados deprediccion son similares aunque con ligera superioridad de la metodologıaDRAG.

2. La metodologıa para seleccion de variables y modelos proporciona resul-tados practicos en cuanto a la explicacion de los accidentes de trafico.

La prediccion y la interpretacion tambien se han mejorado medianteesta nueva metodologıa.

3. Se ha implementado una metodologıa para profundizar en el conocimientode la relacion entre las estimaciones de los efectos de dos modelos com-petidores como DRAG y UCM. Un aspecto muy importante en estetema es la interpretacion de la tendencia mediante dos modelos difer-entes de la que se ha obtenido informacion muy util para los investi-gadores en el campo del modelado.

Los resultados han proporcionado una ampliacion satisfactoria del conocimientoen torno al proceso de modelado y comprension de los accidentes con impli-cacion de furgonetas y accidentes mortales totales en Espana.

Dedicated to my parents and siblings.

Contents

I Accidents and their consequences during the pe-riod 2000-2011. Potential influential factors in roadaccident analysis 1

1 Introduction 31.1 Road accidents . . . . . . . . . . . . . . . . . . . . . . . . . . 31.2 Methodological approach . . . . . . . . . . . . . . . . . . . . . 61.3 Main objectives and the structure of the thesis . . . . . . . . . 8

2 Data set 112.1 Dependent variables . . . . . . . . . . . . . . . . . . . . . . . 11

2.1.1 Fatal accidents . . . . . . . . . . . . . . . . . . . . . . 132.1.2 Van-involved road accidents . . . . . . . . . . . . . . . 13

2.2 Explanatory factors . . . . . . . . . . . . . . . . . . . . . . . . 162.2.1 Exposure . . . . . . . . . . . . . . . . . . . . . . . . . 162.2.2 Economic variables . . . . . . . . . . . . . . . . . . . . 202.2.3 Driver characteristics and surveillance . . . . . . . . . . 272.2.4 Vehicle characteristics . . . . . . . . . . . . . . . . . . 312.2.5 Road infrastructure . . . . . . . . . . . . . . . . . . . . 312.2.6 Legislative measures . . . . . . . . . . . . . . . . . . . 342.2.7 Weather conditions . . . . . . . . . . . . . . . . . . . . 372.2.8 Calendar effect . . . . . . . . . . . . . . . . . . . . . . 40

2.3 Adjusting the data: missing values . . . . . . . . . . . . . . . 402.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

II Computational Tools for the Evaluation and Anal-ysis of Road Safety. 43

3 Statistical methodology 47

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3.1 Functional form . . . . . . . . . . . . . . . . . . . . . . . . . . 473.1.1 Dynamic regression . . . . . . . . . . . . . . . . . . . . 473.1.2 Demand for Road use, Accidents and their Gravity

(DRAG) . . . . . . . . . . . . . . . . . . . . . . . . . . 493.1.3 Unobserved Components Model (UCM) . . . . . . . . . 54

3.2 Model estimation and diagnosis . . . . . . . . . . . . . . . . . 553.2.1 Maximum likelihood estimation . . . . . . . . . . . . . 553.2.2 Markov Chain Monte Carlo estimation . . . . . . . . . 573.2.3 Goodness of fit measures . . . . . . . . . . . . . . . . . 58

3.3 Elasticity estimation . . . . . . . . . . . . . . . . . . . . . . . 613.4 Multicollinearity . . . . . . . . . . . . . . . . . . . . . . . . . 623.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

4 Explanation of van-involved road accident indicators. Model

comparison 654.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 654.2 Van-involved road accidents . . . . . . . . . . . . . . . . . . . 664.3 Independent variables . . . . . . . . . . . . . . . . . . . . . . . 714.4 Model construction and estimation . . . . . . . . . . . . . . . 734.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

4.5.1 Exposure . . . . . . . . . . . . . . . . . . . . . . . . . 814.5.2 Economic factors . . . . . . . . . . . . . . . . . . . . . 814.5.3 Driver behavior surveillance . . . . . . . . . . . . . . . 834.5.4 Fleet characteristics . . . . . . . . . . . . . . . . . . . . 844.5.5 Road infrastructure . . . . . . . . . . . . . . . . . . . . 844.5.6 Legislative measures . . . . . . . . . . . . . . . . . . . 854.5.7 Calendar effect and weather conditions . . . . . . . . . 86

4.6 Prediction analysis . . . . . . . . . . . . . . . . . . . . . . . . 864.7 Summary and discussions . . . . . . . . . . . . . . . . . . . . 91

5 Analysis of fatal accidents: model selection methodology 955.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 955.2 Fatal accidents . . . . . . . . . . . . . . . . . . . . . . . . . . 965.3 Independent variables . . . . . . . . . . . . . . . . . . . . . . . 965.4 Model selection procedure . . . . . . . . . . . . . . . . . . . . 965.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

5.5.1 Explanatory variable selection . . . . . . . . . . . . . . 1025.5.2 Estimation of power transformation parameter . . . . . 1035.5.3 Model selection . . . . . . . . . . . . . . . . . . . . . . 104

5.5.4 Dynamic regression model . . . . . . . . . . . . . . . . 1065.6 Prediction analysis . . . . . . . . . . . . . . . . . . . . . . . . 1105.7 Summary and discussions . . . . . . . . . . . . . . . . . . . . 112

6 Simulation experiment based model comparison methodology

with application to road accident models 1156.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1156.2 Simulation experiment methodology . . . . . . . . . . . . . . . 1176.3 Empirical study . . . . . . . . . . . . . . . . . . . . . . . . . . 118

6.3.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1186.3.2 Model estimation . . . . . . . . . . . . . . . . . . . . . 119

6.4 Experimental design: estimation and results . . . . . . . . . . 1216.4.1 Experimental design . . . . . . . . . . . . . . . . . . . 1216.4.2 Generating UCM samples . . . . . . . . . . . . . . . . 1276.4.3 Estimating DRAG models using the UCM samples . . 1276.4.4 ANOVA . . . . . . . . . . . . . . . . . . . . . . . . . . 1296.4.5 Results of the experimental design-ANOVA . . . . . . 129

6.5 Summary and discussions . . . . . . . . . . . . . . . . . . . . 132

III Conclusions 135

Bibliography 142

Appendix I 157

Appendix II 162

Appendix III 174

Appendix IV 177

Appendix V 187

Appendix VI 193

Appendix VII 211

List of Figures

1.1 Road use indicators: drivers, vehicles and total distance trav-elled vs. road traffic casualities and fatal accidents in Spain1990-2011 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.2 Causes of death for age groups in Spain. Year 2012 . . . . . . 5

2.1 Fatalities in accidents with vehicle type involved.(Index Year2000 = 100.) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.2 Yearly data on fatal accidents, ACCTOT , 2000-2011: all ve-hicle types included. . . . . . . . . . . . . . . . . . . . . . . . 13

2.3 Yearly data on van-involved road accident indicators, 2000-2009: 15

2.4 Exposure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.5 Economic factors. . . . . . . . . . . . . . . . . . . . . . . . . . 25

2.6 Driver characteristics. . . . . . . . . . . . . . . . . . . . . . . . 29

2.7 Vehicle characteristics. . . . . . . . . . . . . . . . . . . . . . . 32

2.8 Road infrastructure. . . . . . . . . . . . . . . . . . . . . . . . 33

2.9 Legislative measures. . . . . . . . . . . . . . . . . . . . . . . . 35

2.10 Weather conditions. . . . . . . . . . . . . . . . . . . . . . . . . 39

2.11 Calendar effect. . . . . . . . . . . . . . . . . . . . . . . . . . . 41

4.1 Decomposition of series into trend-cycle and seasonal compo-nents with TRAMO/SEATS: . . . . . . . . . . . . . . . . . . 70

4.2 Residual analysis of road safety measures. . . . . . . . . . . . 80

4.3 Observed versus predicted values of four road safety indicators,corresponding to year 2009. . . . . . . . . . . . . . . . . . . . 89

4.4 Prediction errors corresponding to quarterly data. . . . . . . . 91

5.1 Decomposition ofACCTOT into trend-cycle and seasonal com-ponents with TRAMO/SEATS. . . . . . . . . . . . . . . . . . 98

5.2 BCT optimization, Yt. . . . . . . . . . . . . . . . . . . . . . . 104

5.3 Prediction intervals for selected models. . . . . . . . . . . . . . 111

xvii

6.1 Simulation methodology. . . . . . . . . . . . . . . . . . . . . 1186.2 Residual analysis of ACCMOR . . . . . . . . . . . . . . . . . 1206.3 Generated samples . . . . . . . . . . . . . . . . . . . . . . . . 1286.4 Interaction plot between D and F , for the DRAG parameter

ηDLAB. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131

List of Tables

2.1 Explanatory factors. . . . . . . . . . . . . . . . . . . . . . . . 17

3.1 DRAG family models. . . . . . . . . . . . . . . . . . . . . . . 503.2 Elasticity estimates for different functional forms (McCarthy ,

2001). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

4.1 Dependent variables. . . . . . . . . . . . . . . . . . . . . . . . 664.2 Summary of TRAMO/SEATS results∗. . . . . . . . . . . . . . 714.3 Explanatory variables, 2000-2009. . . . . . . . . . . . . . . . 724.4 Parameter estimates of DRAG models. . . . . . . . . . . . . . 744.5 Fit statistics of DRAG models. . . . . . . . . . . . . . . . . . 744.6 Fit statistics of UCM components. . . . . . . . . . . . . . . . 754.7 Normality test of UCM errors. . . . . . . . . . . . . . . . . . . 764.8 Exposure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 814.9 Economic factors. . . . . . . . . . . . . . . . . . . . . . . . . . 824.10 Driver behavior surveillance. . . . . . . . . . . . . . . . . . . . 844.11 Fleet characteristics. . . . . . . . . . . . . . . . . . . . . . . . 844.12 Road infrastructure. . . . . . . . . . . . . . . . . . . . . . . . 854.13 Legislative measures. . . . . . . . . . . . . . . . . . . . . . . . 854.14 Calendar effect and weather conditions. . . . . . . . . . . . . . 864.15 A year ahead prediction, year 2009. . . . . . . . . . . . . . . 904.16 Prediction error in percentage for DRAG and UCM. . . . . . 90

5.1 Summary of TRAMO/SEATS results, ACCTOT . . . . . . . . 975.2 Outlier detection. . . . . . . . . . . . . . . . . . . . . . . . . . 975.3 Explanatory variables, 2000-2011. . . . . . . . . . . . . . . . 995.4 Stage 1: Pseudo-R2 values of selected two-input models for

three different values of power transformation, λX . . . . . . . . 1025.5 Explanatory variables selection. . . . . . . . . . . . . . . . . . 1035.6 Selected variables and the expected signs, based on previous

empirical studies. . . . . . . . . . . . . . . . . . . . . . . . . . 105

xix

5.7 Fit statistics of selected 10 SE models. . . . . . . . . . . . . . 1055.8 Fit statistics of DR models. . . . . . . . . . . . . . . . . . . . 1075.9 Estimation results of selected models, DR2 and SE207. . . . . 1075.10 Posterior prediction intervals of selected models. . . . . . . . . 1095.11 Prediction accuracy of selected models . . . . . . . . . . . . . 110

6.1 Explanatory variables. . . . . . . . . . . . . . . . . . . . . . . 1196.2 Results of empirical study: fit statistics and parameter estimates.1216.3 Parameter estimates. . . . . . . . . . . . . . . . . . . . . . . . 1226.7 DRAG estimation. . . . . . . . . . . . . . . . . . . . . . . . . 1266.8 Significant main effects for DRAG parameters. . . . . . . . . . 1306.9 Analysis of variance: ηPARSER . . . . . . . . . . . . . . . . . . 2126.10 Analysis of variance: ηCONALC . . . . . . . . . . . . . . . . . . 2136.11 Analysis of variance: ηSUSP . . . . . . . . . . . . . . . . . . . 2146.12 Analysis of variance: ηDLAB . . . . . . . . . . . . . . . . . . . 2156.13 Analysis of variance: ηCOMTOT . . . . . . . . . . . . . . . . . . 2166.14 Analysis of variance: ρ1 . . . . . . . . . . . . . . . . . . . . . . 2176.15 Analysis of variance: ρ2 . . . . . . . . . . . . . . . . . . . . . . 2186.16 Analysis of variance: λ . . . . . . . . . . . . . . . . . . . . . . 219

Part I

Accidents and their

consequences during the period

2000-2011. Potential influential

factors in road accident analysis

1

Chapter 1

Introduction

1.1 Road accidents

During the last two decades very important policy measures have been im-plemented by the respective administrations in Spain with the purpose ofimproving the road safety. These measures have been intensified since Jan-uary 2003. In July 2006 and December 2007 two most important policy mea-sures, the Penalty Point System and the Penal Code Reform were enactedrespectively. Other preventive and corrective strategies were also conductedduring 2005-2008, in the framework of Road Safety Strategic Plan, e.g., amore intense monitoring of speed, alcohol or drug use, media coverage ofsafety items, etc. As it can be observed in Figure 1.1 1, all these factors havethus helped in the improvement of road safety measures in Spain. Between2001 and 2010, the total number of fatal accidents decreased from 4,170 to1,953 (53% decrease) and the number of road fatalities from 5,516 to 2,479(55%).

The last two decades are also characterized by the intensified road net-work use and increasing exposure, as it can be seen in the same figure. Thenumber of travelers in transport has doubled during 1997-2007 in Spain, hav-ing in turn a significant economic, social and environmental impact. It isestimated that, currently, there are 31 million vehicles circulating in Spain,driven by more than 26 million drivers in more than 165,000 km of roads(Lopez and Skowronek , 2014). These figures (except for road length) do not

1 The data for fatalities, driver census and vehicle fleet are obtained from Directory of

General Traffic while the mobility data were obtained from Ministry of Public Works and

Transport

3

Chapter 1. Introduction 4

Fig. 1.1. Road use indicators: drivers, vehicles and total distance travelled vs. road

traffic casualities and fatal accidents in Spain 1990-2011

represent exposure caused by tourists visiting the country, that estimated tobe more than 60 million during 2013 alone.

The increasing number of road users and the exposure can jeopardize theeffect of road safety measures. The injury and the loss of human life are theprimary damages inflicted by accidents. In spite of the improving road safetyindicators, as mentioned above, the consequences of road accidents such asthe number of deaths and injured victims are still very high. It is estimatedthat in 2013 the total number of deaths in Spanish roads has been 1,680. Thenumber of seriously injured as the result of traffic accidents is even higher,19,508. In general, worldwide, more than 1.2 million people die annuallyin highway-related crashes and as many as 20-50 million are injured (WorldHealth Organization , 2013). It is estimated that by 2030 road accidents willbe the 5th leading cause of death in the world (World Health Organization ,2013). In Spain, road accident-related fatalities are one of the leading causesof death, specially among the younger age groups (Figure 1.2 2). It is the

2National Institute of Statistics (INE).

5 1.1. Road accidents

Fig. 1.2. Causes of death for age groups in Spain. Year 2012

first cause of death for age groups 20-24. And for the age group 30-39, roadaccidents have been the third leading cause of death in 2012. The averageage of death as a result of road accidents is around 50 years old. This showsthat the main victims of the road accidents are the working-age group, whichbesides the human loss also has a negative impact on the economy. Moreover,road accident-related injuries cause a great problem on the health system of astate. The impact of road traffic accidents on the economy is thus inevitable.It is estimated that, on average, their total costs, including an economicvaluation of lost quality of life, are about 2.5% of the gross domestic product(GDP) (Elvik , 2000). Excluding the valuation of lost quality of life, roadaccident costs on average amount approximately to 1.3% of the GDP.

Thus, road safety remains one of the priorities and is still pending of fur-ther improvements, which is a goal followed by safety-concerned state admin-istrations and international non-governmental organizations. This problemcan be solved through different means but all should be scientifically sound.The data collected from reliable sources should be analyzed using the mostadequate scientific and statistical methodologies in order to study road safetyindicators, with the purpose of reducing road accident frequency and severity.


1.2 Methodological approach

Accidents are the outcome of a complex random process, whose general char-acteristics can be modelled statistically (Elvik and Vaa , 2004, Washingtonet al. , 2011). The research on road accidents has one specific goal: to im-prove the road safety, hence the main factors causing this phenomenon shouldbe clearly stated and studied. Many empirical studies have tried to explaintraffic accident data by means of different factors. These factors are referredto as explanatory factors or variables. The estimation of the effect of theselected factors and policy measures on road safety is conducted by meansof econometric models whose main task is to describe, explain and predictroad safety developments (Hakim et al. , 1991). As road safety indicators,normally the frequency (accident count) and severity (victim count) of theaccidents are assessed. In the econometric model these measures take up therole of the response, while the explanatory factors take up the role of the re-gressors (predictors). In general the accident data can be categorized as timeseries, cross sectional or panel data, with the time-series data being mostlyused.

The choice of the econometric model to be used for the estimation ofroad accident frequency and severity depends on the data available to theresearcher. Given that road accident data are usually count data, where theobservations take only non-negative, integer values, the Poisson regressionhas served as a basis for some initial research study in road safety analysis(Abdel-Aty and Radwan , 2000, Fridstrøm et al. , 1995, Hauer , 2001, 2004,Hauer et al. , 2004, Ivan et al. , 2000, Jovanis and Chang , 1986, Knuimanet al. , 1993, Lord et al. , 2005, Lord and Mannering , 2010, Miaou , 1996,Miaou et al. , 1992, Miaou and Lum , 1993, Milton and Mannering , 1998,Poch and Mannering , 1996, Shankar et al. , 1997). The Poisson process isthe continuous time analog of Bernoulli trials and was investigated by theFrench mathematician Simon Denis Poisson (1781–1840). The Bernoulli trialis an experiment with two possible outcomes: success and failure. Thus it ismore appropriate to use Poisson models for micro (disaggregated) data, suchas number of accidents in a given intersection, severity of accidents in a givenroad section, etc. The Poisson model is used when the mean and varianceof the accident frequencies are approximately equal. A relatively longer timeseries data will be Poisson distributed. However in practice the actual dataseries is not so long, thus problems such as over-dispersion, i.e. a significantlyhigher variance, may arise. For such kind of data it is more appropriate touse a negative binomial model.

7 1.2. Methodological approach

Although the Poisson distribution structure is appropriate for countdata, it is not able to take into account the autocorrelation observed in themost time series data. The autocorrelation is observed when the error termsare correlated over time. The persistence of this problem in the model couldresult in biased estimates of the coefficients thus affecting the interpreta-tion and the prediction accuracy. The error autocorrelation can happen dueto different reasons; one is the explanatory factors present in an accidentmodel, specially if there is a lagged relationship between these factors andthe dependent variable. This phenomena can be modelled through dynamicregression (DR) or transfer functions where the autocorrelated error termis assumed to follow the Box and Jenkins autoregressive integrated movingaverage (ARIMA) process (Box and Jenkins , 1970). The DR models havebeen frequently applied in road safety analysis, specially where the effect ofmacro-economic factors and policy measures on the road safety indicators hasbeen studied (Garcıa-Ferrer et al. , 2006, 2007).

A different model type, that has been used in road safety analysis is theDRAG (demand for road use, accidents and their gravity) models developedby Gaudry (1984) and Gaudry and Lassarre (2000), where the error au-tocorrelation is treated through autoregressive process. The DRAG modeltries to explain accidents for a whole region, province or a country and definethe role the external factors play in the occurrence of accidents. In generalDRAG strategy is described as i) formulation of the problem and simulationof a system of equations which is typically estimated recursively; ii) decom-posing the damage outcomes (victims) by category; iii) making extensive useof Box -Cox transformation; iv) producing correlation signs, coefficients andassociated elasticities which show the relationship between the external fac-tors on traffic accidents and their severity. The original DRAG model wasdeveloped for Quebec, Canada and consists of a five layer procedure to ex-plain the impact of several factors on monthly demand for road use and thenumber of road accident victims, during the period of 1956-1982. Later on,DRAG-inspired models were developed for other parts of the world such asNorway (Fridstrøm , 2000), Stockholm (Tegner and Loncar-Lucassi , 1997),France (Jaeger and Lassarre , 2000), Germany (Blum and Gaudry , 2000),California (McCarthy , 2000), Spain (Aparicio et al. , 2013), Algeria (Gaudryand Himouri , 2013), which altogether make up the DRAG-family (Table 3.1)(see Section 3.1.2.2).

Yet another cause of serial autocorrelation is to be found in the natureof the time series. For monthly data, which is most commonly used for acci-dent analysis, trend and seasonality contribute to serial correlation. In order


to take these factors into account Harvey and Durbin (1986) developed astructural descriptive model with intervention variable, where the variancepresent in the data is filtered out by incorporating trend and seasonality asunobserved components into the model. UCM was first used to estimate theimpact of the seatbelt law on road safety in Great Britain. The authors intro-duce the seatbelt law enforced by the British Government as an interventionvariable. The further development of the UCM is studied in Commandeurand Koopman (2007), Durbin and Koopman (2001). The applications ofUCM in road safety have been carried out by several authors, among themScuffham and Langley (2002) use UCM to model the traffic crashes in NewZealand; Hermans et al. (2005, 2006) have used the UCM methodology toestimate the effect of road safety measures on the monthly frequency andseverity of road traffic accidents in Belgium; Bijleveld et al. (2008, 2010)use the state-space model for measuring exposure and risk for fatal road ac-cidents; Aparicio et al. (2011), Castillo-Manzano et al. (2010, 2011) haveapplied the UCM methodology to analyze the effect of the Penalty PointSystem and the Penal Code Reform on traffic accidents in Spain.

In spite of the ever improving methodological developments and innova-tions in road safety study there still remain some issues that have not beencompletely addressed in road safety literature. Some of these issues are themethodological choice, model selection and comparison. The lack of researchin these areas has been pointed out in the most recent study by Manneringand Bhat (2014). In addition to carrying out the macro analysis of the roadsafety indicators in Spain, this thesis has been developed with the objectiveof providing some insight, both empirical and theoretical, into these topics.The main objectives of the thesis are detailed in the following section.

1.3 Main objectives and the structure of the

thesis

The main goal of this thesis is the analysis of road safety issues in Spain,since 2000. This period is mainly characterized by a major improvement inroad safety policy by the Spanish authorities, and a significant change in theeconomic situation of country. In order to analyze the impact of these andother macro factors on road accidents, as well as to propose some method-ological developments, several road safety indicators have been studied. Inthis thesis mainly two data sets, consisting of five road safety indicators, havebeen used in the applications: 1) the total figures for fatal accidents; and 2)

9 1.3. Main objectives and the structure of the thesis

figures related to frequency and severity of van-involved accidents.

The objectives of the thesis are divided into two blocks: empirical anal-ysis and two methodological developments. Both blocks provide an extensiveliterature review of existing studies on the topic. The objective of the firstblock, empirical analysis, is to achieve a better understanding of the roadaccident phenomenon by means of the application and comparison of two ofthe most frequently used macro modeling: DRAG and UCM. The researchwas carried out using monthly data indicating the frequency and severity ofvan-involved road accidents in Spain, during 2000-2009. The main contribu-tion of this research work, apart from providing interpretation and predictionfor van-accident behavior, is the model comparison exercise. It is in generalevident that the choice of statistical methodology used in road safety stud-ies will depend on the data. However, even with the same database, modelcomparison can leave much to be desired as far as the statistical evidence isconcerned. This thesis thus tries to provide an insight on the topic of com-parison of two different types of models: explanatory and descriptive models.

Following the findings in the first block and considering some drawbacksof the model selection and comparison process, the second block objectiveswere proposing two methodological developments: 1) model selection method-ology and; 2) simulation-based model comparison methodology.

The first methodological development was carried out using data on fatalaccidents in Spain during 2000-2011. The main objective of the research workwas proposing a model selection procedure, i.e. selection of variables and pa-rameter estimation. Following the results of the previous research work, forthis exercise, the DRAG-like methodology, the structural explanatory model(SE), was used. The estimation was carried out within the Bayesian frame-work. The results of the model selection procedure are compared and vali-dated through prediction and comparison with those of the DR model, giventhat the original data has a stochastic trend. The main contribution of thiswork is the model selection procedure called TIM (named after two-inputmodel, since the initial models used for variable selection use two inputs)that proves to be efficient. Moreover the results provide a better understand-ing and interpretation of fatal road accidents in Spain during the last decade.

Simulation-based model comparison methodology was carried out usingMonte Carlo simulation, computer experiment design and ANOVA. The mainobjective was to see how one type of model can be interpreted through anothertype. This study also tries to take into account the question emerged duringthe second study, i.e. how the DRAG or SE modeling should be carried outif the data includes a stochastic trend component. Considering that UCM


includes a specific stochastic trend term the comparison was carried out usingUCM as a true data generating process and carrying out estimation throughDRAG model. The simulation was carried out using the parameter estimatesthe UCM of the first study. In order to generate a stochastic process anadditional trend term was added. The main contribution of this researchwork is to provide a model comparison methodology that can be carried outwith the existing statistical tools. Moreover the findings suggest that evenif the model estimation can provide reliable goodness of fit measures, theexisting stochastic component should be modelled appropriately in order toprovide unbiased estimates.

The structure of the thesis closely follows the main goals and objectivesdescribed above. The thesis is divided into three parts that consists of 6chapters and Conclusions as described below:

Part I : Accidents and their consequences in the period 2000-2011. Potentialinfluential factors in accident analysis.

Chapter 1. Introduction.

Chapter 2. Data sets.

Part II : Computational Tools for the Evaluation and Analysis of Road Safety.

Chapter II. Introduction.

Chapter 3. Statistical methodology.

Chapter 4. Explanation of van-involved road accident indicators. Model com-parison.

Chapter 5. Analysis of fatal accidents: model selection methodology.

Chapter 6. Simulation experiment based model comparison methodology withapplication to road accident models.

Part III : Conclusions, contribution and future work

Chapter 2

Data set

This chapter discusses the data sets used in this study. For the empiricalstudy two sets of dependent variables are used: 1) van-involved road accidentsin Spain, covering the period of 2000-2009; and 2) total number of fatalaccidents in Spain, covering the period of 2000-2011. Both data sets wereobtained from the General Database owned by General Directorate of Traffic(DGT) in Spain. The first set, the van-involved road accidents, was studiedusing four monthly time series data for vans: 1) number of van-involved fatalaccidents; 2) number of van-involved accidents with seriously injured people;3) number of fatalities in van-involved accidents and; 4) number of seriouslyinjured people in van-involved accidents whereas the second set consists of onemonthly time series. In the next section both of the data sets are presented.The dependent variables will be presented in the next section.

The above indicated road safety measures are modelled using an exten-sive set of explanatory factors (independent variables) which is aggregated atthe country level. The independent variables will be presented in section 2.2of this chapter.

2.1 Dependent variables

Spain reached the European Union target of achieving a 50% reduction inthe number of road fatalities during 2001-2010, following Latvia, Estonia andLithuania (European Transport Safety Council , 2011). As it was pointed outin Introduction road safety policy has experienced a major political changesduring the last decade and different legislative measures as well as preventiveand corrective strategies have been conducted. Another factor that has also

11

Chapter 2. Data set 12

Fig. 2.1. Fatalities in accidents with vehicle type involved.(Index Year 2000 = 100.)

greatly affected the road safety measures in Spain during this period is theeconomic crisis and its consequences. In order to evaluate the effect of policymeasures and different macro economic factors on the decreasing number offatal accidents a new study was conducted, the main purpose of it being thedetermining the number of factors that have had a significant impact on theroad safety indicator, ACCTOT (see Section 2.1.1).

However the significant decrease observed in the number of fatal ac-cidents was not the case for the van-involved road accidents. Comparingthe road safety indicators across the vehicles it was observed that the num-ber of fatal accidents decreased by 57% and by 56% in passenger cars andlarge trucks respectively, while in van-involved fatal accidents only a 33%decrease was observed. As for the number of fatalities, there was a 38%decrease in van-involved accidents, while for passenger cars and trucks thefigures were 58% and 59% respectively (Figure 2.1). In order to understandthe factors influencing van-involved crashes, a research was carried out bythe researchers led by the Technical University of Madrid, during 2009-2011(FURGOSEG , 2011). The main objective of the research was, using the dataon van-involved road accidents, to determine the main causes of van-involvedaccidents through macro models, where the effect of different macroeconomicfactors, as well as policy measures were assessed (see Section 2.1.2).

13 2.1. Dependent variables

Fig. 2.2. Yearly data on fatal accidents, ACCTOT , 2000-2011: all vehicle types

included.

2.1.1 Fatal accidents

The number of fatal accidents in Spain, ACCTOT , is studied during theperiod of 2000-2011 (Figure 2.2). The main purpose of the research workwas assessing the factors that have affected to the decreasing number of fatalaccidents in Spain. For this purpose a model selection methodology was pro-posed. The methodology is based on SE models where the MCMC methodswere used for the model estimation and selection. The results of the modelselection methodology were compared to those of DR model. The proposedmethodology and its results where the number of fatal accidents were studiedwill be presented in chapter 5.

2.1.2 Van-involved road accidents

Van-involved accidents in Spain during the period of 2000-2009 were stud-ied in detail. For this purpose, four monthly time-series were considered fordata analysis: number of fatal accidents (ACCMOR); number of accidentswith seriously injured people (MORHER); number of fatalities (MUER)and number of seriously injured people (HERGRA) (Figure 2.3). In order


2.3.a

2.3.b

15 2.1. Dependent variables

2.3.c

2.3.d

Fig. 2.3. Yearly data on van-involved road accident indicators, 2000-2009:

2.3.a)ACCMOR; 2.3.b)MORHER; 2.3.c)MUER; 2.3.d)HERGRA.


to carry out the macro analysis, different methodologies were applied. Themain purpose of the research work was the explanation of the van-involvedroad accidents through different methodologies. For this purpose two dif-ferent macro models were used: DRAG and UCM. The comparison of twomodels was carried out both empirically and mathematically. The empiricalcomparison was carried out using the observed data for both models. Themathematical comparison of the two models was carried out using the simu-lated data. The empirical and mathematical study and their results will bepresented in chapters 4 and 6 respectively.

2.2 Explanatory factors

A road safety measure (e.g. frequency and severity) is modelled as a func-tion of different socio-economic factors. Although there is no well-establishedtheory indicating which factors should be included in a selected model, fac-tors causing the traffic crashes can be classified into different categories andstudied in an aggregate. The independent variables used in this chapter aredivided into following categories: exposure, economic factors, driver char-acteristics and surveillance, vehicle characteristics, road infrastructure, leg-islative measures, weather conditions and calendar effect (Table 2.1). Thegeneral data were obtained from the DGT, the Ministry of Public Works, theNational Meteorological Office, the National Statistics Office and the Min-istry of Economy and Finance. Since the data on explanatory variables arecollected from different sources that are not conditional on crash occurrencethe problem of the estimation bias is not present in this case (Anastasopoulosand Mannering , 2011, Mannering and Bhat , 2014).

2.2.1 Exposure

The measure of exposure is generally defined as the amount of travel within atraffic system Hakkert and Braimaister (2002). Exposure can also be referredas the traffic volume (Elvik et al. , 2009). The various ways of measuringthe amount of travel are referred to collectively as exposure data because theymeasure traveler’s exposure to the risk of death or injury (European TransportSafety Council , 1999). The most common method of measuring exposure isto use the kilometers/mileage travelled. The other means of measuring theexposure includes factors such as traffic volume and fuel consumption. Theexposure variable can also be represented using the rates, such as kilometers

17 2.2. Explanatory factors

Table 2.1: Explanatory factors.

Variable Definition Period Mean (in units)

Exposure

VHP Heavy Vehicles 2000-2011 2549 ·103

PRGFUR Van Fleet 2000-2009 2489 ·103

VKM Vehicle Kilometers Travelled 2000-2011 1472 ·106

CONOIL Diesel Consumption 2000-2011 1838 ·103 tons

CONGAS Gasoline Consumtion 2000-2011 609 ·103 tons

COMTOT Total Fuel Consumption 2000-2011 2455 ·103 tons

Economic factors

IPI Industrial Production Index 2000-2011 95 (Index)

INDVEN Sales Index 2000-2011 93 (Index)

INDCOM Commerce Index 2000-2009 96 (Index)

PRDCRN Meat Production 2000-2011 457 ·103 tons

CONCEM Cement Consumption 2000-2011 3464 ·103 tons

MANT Maintenance Investment 2000-2011 790 euro per km

CONST Construction Investment 2000-2011 299 ·103 euro

PRECOM Fuel Price 2000-2011 7 cent per km

INDACT Activity Index 2000-2009 97 (Index)

OCUP1 Total Employed 2000-2011 18 ·106

OCUP2 Employment Construction Sector 2000-2011 15 ·105

PARO Total Unemployment 2000-2011 1943 ·103

PARSER Unemployment Service Sector 2000-2011 1528 ·103

Driver characteristics

and surveillance

COND2 Young Drivers (2 years) 2000-2011 1341 ·103

CONALC Random Alcohol Checks 2000-2011 285 ·103

RADAR Speed Controls 2000-2011 1763 ·103

PRADAR Positives in Speed Controls 2000-2011 3 (%)

SUSP Driving License Suspended 2000-2011 13 ·103

PRLSUSP Driving License Suspended (B and B1 type) 2000-2011 9 ·103

Vehicle characteristics

VEH10 Vehicle Age (10 years), % of Total Fleet 2000-2011 36 (%)

AIRBAG Airbag Equipped, % of Total Fleet 2000-2009 41 (%)

ABS ABS Equipped, % of Total Fleet 2000-2011 45 (%)

Road infrastructure

LONRAC High Capacity Roads, % of Total Network 2000-2011 6 (%)

LONRED Length of Toll Roads 2000-2011 2215 km

Legislative measures

PPS Penalty Point System 2000-2011 Dummy

RPC Penal Code Reform 2000-2011 Dummy

RUIDO Safety Items in Press 2000-2009 311 (Index)

Weather conditions

PREC Rainfall 2000-2011 50 mm

DNIE Number of Snowing Days 2000-2011 0,2 day

DNIEB Foggy Days 2000-2011 2 days

SLNV Number of Days with Snow Covered Ground 2000-2011 0,1 day

HSOL Amount of Sunny Hours 2000-2011 217 hr

TEMP Average Temperature 2000-2011 15 ◦ C

Calendar effect

DLAB Working days 2000-2011 20 days

SDF Weekend and Holidays 2000-2011 9 days

SEMSAN Easter Break 2000-2011 Dummy


2.4.a

2.4.b

2.4.c


2.4.d

2.4.e

2.4.f

Fig. 2.4. Exposure.

2.4.a)V HP ; 2.4.b)PRGFUR; 2.4.c)V KM ; 2.4.d)CONOIL; 2.4.e)CONGAS;

2.4.f)COMTOT .


traveled per vehicle, fuel consumption per capita, etc. There is a straightfor-ward relationship between the exposure and the accident risk, i.e. higher theexposure, greater is the rate of accident occurrence.

In this study exposure is measured through fleet volume of heavy vehi-cles, V HP , and vans, PRGFUR, vehicle kilometers travelled V KM , fuel con-sumption: diesel consumption (CONOIL), gasoline consumption (CONGAS)and total fuel consumption (COMTOT ) (Figure 2.4). It can be observed thatPRGFUR has an increasing trend during 2000-2007. The average annual in-crease during this period has been 2.58%. The trend starts to decline from2007 on, with average rate of 6.39%. The van fleet however has an increasingtrend during 2000-2009, with the average annual rate of 5.54%. The timeseries for V KM exhibits a strong seasonal pattern with an increasing trendtill 2007, for which the annual average has been 6.41%. The trend starts todecrease from 2007 on with an average of 4.75%. The diesel and total fuelconsumption has an increasing trend till 2007 (6.23% and 3.55% increase onaverage respectively) followed by a decreasing trend since 2008 (3.37% and3.81% decrease respectively). The consumption has a decreasing trend withthe average annual rate of 4.24%.

2.2.2 Economic variables

The economic factors have a major influence on road safety and its impacthas been vastly analyzed in road safety literature. The effect of economy onroad safety can be categorized as short term and long term impact. Increas-ing economic situation of household has a negative impact on road safety inshort run (Fridstrøm , 2000, Garcıa-Ferrer et al. , 2006, Loeb and Clarke, 2007, Scuffham and Langley , 2002). This is explained by the fact thatincreasing household income will affect to the demand for cars and thus ex-posure. However in a long run, the economic growth can increase the roadsafety (Fridstrøm , 1999, Hakim et al. , 1991), since as the economic growthimproves the investment for the transport related infrastructure will increaseas well. It has been shown that generally the economic cycles and traffic ac-cidents have a common trend during major recessions and expansions (Evansand Graham , 1988, Garcıa-Ferrer et al. , 2006).

The short term effect of economy on road safety is analyzed throughindustrial production index (IPI), sales index (INDV EN), commerce index(INDCOM), meat production (PRDCRN), cement consumption (CONCEM),while the long term effect is estimated using the investment on road con-struction (CONST ) and maintenance (MANT ) (Figure 2.5). Three of the


2.5.a

2.5.b

2.5.c


2.5.d

2.5.e

2.5.f


2.5.g

2.5.h


2.5.i

2.5.j

2.5.k


2.5.l

2.5.m

Fig. 2.5. Economic factors.

2.5.a)IPI; 2.5.b)INDV EN ; 2.5.c)INDCOM ; 2.5.d)PRDCRN ;

2.5.e)CONCEM ;; 2.5.f)PRECOM ; 2.5.g)MANT ; 2.5.h)CONST ;

2.5.i)INDACT ; 2.5.j)OCUP1; 2.5.k)OCUP2; 2.5.l)PARO; 2.5.m)PARSER.


variables representing indices of economic situation (IPI, INDV EN andINDCOM) have a seasonal pattern with similar behavior. The trend forthree variables is increasing till 2007 (1.19%, 2.92%, and 2.43% on averagerespectively) that starts to decrease from 2008 on, with the average annualrate of 6.01%, 4.95% and 5.68% respectively. The PRDCRN also exhibit aseasonal pattern with a slightly increasing trend till 2007 (1.97% increase onaverage) that starts to decrease during 2008-2009, with the average annualrate of 7.53%. The trend is increasing from 2009 on with the average annualrate of 3.38%. CONCEM is increasing till 2007 with the average annualrate of 5.52%. After this period there is a sharp reduction till 2011, with theaverage rate of 21%.

Both MANT and CONST experience a stepwise increasing trend till2009. The average increase rate during this period is 5.36% for MANT and3.44% for CONST . The trend starts to decrease till 2011 with the averagerate of 5.14% and 13.72% respectively.

Other economic factors used for the estimation of road safety are fuelprices, PRECOM . According to most studies carried out on traffic accidentsthe increase in fuel prices improves road safety (Chi et al. , 2010, 2013, Gaudryand Lassarre , 2000, Grabowski and Morrisey , 2004, 2006, Hyatt et al. , 2009,Portney et al. , 1991, Wilson et al. , 2009). This factor has specially beenobserved in the case of the fatal accidents. It has been indicated that thereare three intermediate factors through which the increasing fuel prices effectto fatal accidents and fatalities Chi et al. (2010), Gaudry and Lassarre(2000):

• the users drive in a more flexible fashion, which engenders a reductionin road risk;

• the users compensate for the rise in price by a consequent reduction inexposure;

• the users reduce their speed in order to lower their fuel consumption.

The third group of economic factors is the economic activity of the house-holds: activity index (INDACT ), total number of employed (OCUP1), em-ployed in construction sector (OCUP2), total unemployment (PARO) andunemployment in service sector (PARSER) (Figure 2.5). The economic ac-tivity variables INDACT , OCUP1 and OCUP2 are expected to increasethe accident rate. This is explained by a number of factors such as increasinghousehold income, longer journeys and higher exposure, which would have anegative effect on traffic safety (Fridstrøm , 2000). It can be observed that


these three variables are increasing during 2000-2007, with the average rate2.50% for INDACT , 3.96% for OCUP1 and 6.10% for OCUP2 respectively.The trend starts to decrease during 2008-2011, with the average annual rateof 1.96%, 3.68% and 18.16% for INDACT , OCUP1 and OCUP2 respec-tively. Likewise, PARO and PARSER have a decreasing effect on accidentrisk, i.e. as the number of unemployment increases the rate of accidents de-crease (Chi et al. , 2010, Gaudry and Lassarre , 2000, Hakim et al. , 1991,Joksch , 1984, Scuffham and Langley , 2002). Theoretically the unemploy-ment rate will have a positive effect on road safety (Chi et al. , 2010, Gaudryand Lassarre , 2000, Hakim et al. , 1991, Newstead et al. , 1995, Scuffhamand Langley , 2002, Wagenaar , 1984). The total unemployment, PARO hasa slightly increasing trend during 2000-2004 (1.77%). The trend decreasesduring 2005-2007 with the rate of 2.23% on average. The trend starts toincrease again during 2008-2011 (18.33% in average). The unemployment inthe service sector, PARSER, has an increasing trend during 2000-2007. Theaverage annual rate during this period is 1.50%. During 2008-2011 the num-ber of unemployed in service sector decreases sharply, with the average rateof 18.41%.

2.2.3 Driver characteristics and surveillance

Driver characteristics and surveillance refer to the variables associated withthe age and risky behavior of drivers and the surveillance measures taken toprevent it. The driver skills are significant factors in estimation of accidentrisk. In order to estimate the effect of driving skills on road accident measuresthe driver experience, COND2, is considered, which shows the number ofdrivers who have obtained the driving license during the last two years priorto the data collection. It can be observed that the trend for COND2 isgradually increasing till 2008, with the average annual rate of 4.56%. Thetrend starts to decrease abruptly for the rest of the series, 2009-2011, at anaverage rate of 22.27% (Figure 2.6).

The surveillance of risky driver behavior is an important factor to bestudied. This factor is represented by the control on alcohol consumption,CONALC, radar checks, RADAR, percentage of positives in radar checks,PRADAR, driving license suspension, SUSP and suspension of type B andB1 licenses, PRLSUSP . An increase in the alcohol consumption has a di-rect impact on the road risk indicators (Evans , 1990, Hoxie and Skinner ,1987, Loeb , 1987, Ross et al. , 1981, Zlatoper , 1984). The U.S. Depart-ment of Transportation estimates that alcohol is present in roughly 8% of all


2.6.a

2.6.b

2.6.c


2.6.d

2.6.e

2.6.f

Fig. 2.6. Driver characteristics.

2.6.a)COND2; 2.6.b)CONALC; 2.6.c)RADAR; 2.6.d)PRADAR; 2.6.e)SUSP ;

2.6.f)PRLSUSP .


crashes. According to the estimates by DGT alcohol and illegal drugs havebeen found in 42% of deaths in road accidents. Alcohol has particularily sig-nificant impact on fatal accidents. For example, the literature review doneby Moskowitz et al. (1974) shows that alcohol was present in 23% of thedrivers in fatal accidents. In another study conducted by Haworth et al.(1997) it is shown that illegal blood alcohol concentration (BAC) level > 0.05were found in 35% of drivers of fatal crashes. The data shows that the controlon alcohol consumption (random breath tests) is increasing with the averageannual rate of 14.38% during 2000-2011. Moreover we can observe a seasonalpattern, with the peaks occurring during the summer months.

The relationship between the speed and the road risk is relatively intu-itive: ”The more the user increases the speed the less he can take the effec-tive action against any disruption in his environment” (Jaeger and Lassarre ,2000). It has been stated that there is an increasing relationship between thehigher speed and severity of the accidents ( Chen et al. , 2000, Gaudry andLassarre , 2000). That is the reason why almost 22% of the accident relatedfatalities have been caused by inadequate speed. There has been an extensiveresearch on trying to systemize how the speed enforcements affects the roadsafety (Brackett and Edwards , 1977, Elvik , 1997, Finch , 1994, Hauer etal. , 1982, McCarthy , 1994, Østvik and Elvik , 1991, Tay , 2000, Tayloret al. , 2000). The surveillance on speed can take effect through differentmethods, such as mobile radars, speed enforcement cameras, etc. A numberof studies have analyzed the effectiveness of these methods on the reductionof the speed and thus the traffic accidents ( Chen et al. , 2000, Goldenbeldand Van Schagen , 2005, Hirst et al. , 2005, Wilson et al. , 2006). In thisstudy, as speed control variable the data from radar checks have been ana-lyzed. It can be observed that RADAR is mainly increasing with the averageannual rate of 5.99%. PRADAR is however decreasing till 2006 with the av-erage annual rate of 2.93%. The trend starts to increase from 2006 on, withthe average rate of 3.50%. Both RADAR and PRADAR have a somewhatseasonal pattern.

The suspension of driving licenses, SUSP , has similarly been found tobe effective in reducing traffic accident frequency, since the number of crashesincreases with all driving offences (Siskind , 1996). The trend for SUSP ismainly increasing, with the average annual rate of 6.87% during 2000-2011.PRLSUSP has an increasing trend with the level shift during year 2009. Theaverage annual increase rate till this period is 7.59%. After the level shift,which accounts for 26.90% decrease in one year (2009-2010), the trend startsto increase again, with the average rate of 7.97%, during 2010-2011.


2.2.4 Vehicle characteristics

Fleet characteristics represent the older vehicles and the safety devices thevehicles are equipped with. This category includes the percentages of fleet vol-ume equipped with an antilock brake system device, ABS, airbag AIRBAGand percentage of vehicles older than > 10 years, V EH10 (Figure 2.7). Thenumber of vans equipped with ABS devices has been developed by IEA(2009) which was part of the research team of the FURGOSEG (2011)project. The volume of fleet equipped with both of the devices show anincreasing trend. The percentage of total fleet equipped with AIRBAG hasincreased from 9% to 61% during 2000-2009 (18.50% per year on average),while the proportion of total fleet equipped with ABS has increased from10% to 69% (16.28% per year on average) during 2000-2011.

The impact of older vehicles on road safety in Spain has been studied byMendez et al. (2010). The existing literature on road safety shows that thevehicle age is usually associated with increasing rates of accident frequency(Blows , 2003, Mendez et al. , 2010), thus an increasing number of oldervehicles can have a negative impact on road safety. The percentage of thetotal fleet representing vehicle older than 10 years is increasing till 2004, withan average rate of 3.53%. The trend is decreasing during 2004-2007 with anaverage rate of 2.72%. This however is followed by an increasing trend againstarting from 2008 on (5.91% per year on average).

2.2.5 Road infrastructure

The studies related to the road safety consider the road infrastructure asone of the most important factors affecting the traffic accident frequencyand severity. Road infrastructure can be represented both by the geometricdesign of the road and the investment expenditure on the road infrastructure.Normally the latter factor would be considered and studied as an economicfactor (CONST and MANT ). Most of the studies on road infrastructurehave focused on specific design elements such as cross section design, roadsidefeatures, lane width, pavement condition, etc. and tried to quantify theirpotential to reduce the accident rate. Early studies include the work byAgent and Deen (1976), Jovanis and Chang (1986), Knuiman et al. (1993),Miaou et al. (1992) and Milton and Mannering (1998). One of the mostimportant findings of these studies is related to the lane width and numbers.The results show that a narrow lane width and number of lanes increase theaccident occurrence (Abdel-Aty and Radwan , 2000, Milton and Mannering ,1998, Noland , 2001, 2003). On the other hand it has been shown that wider


2.7.a

2.7.b

2.7.c

Fig. 2.7. Vehicle characteristics.

2.7.a)AIRBAG; 2.7.b)ABS; 2.7.c)V EH10.


2.8.a

2.8.b

Fig. 2.8. Road infrastructure.

2.8.a)LONRAC; 2.8.b)LONRED.


medians reduce the frequency of the accident rate, thus improving road safety(Anastosopoulos et al. , 2007, Karlaftis and Golias , 2002, Knuiman et al. ,1993, Noland , 2003).

The variables representing the road infrastructure in this study are theproportion of length of the high capacity roads in the whole interurban net-work, LONRAC, and of the toll road network, LONRED (Figure 2.8).LONRAC is considered as a proxy to the median lane width, i.e. it rep-resents the length of the high capacity roads with higher median width. Theproportion of high capacity roads in the total network has an increasing trend,with the average rate of 4.47%. The toll roads are characterized by less traf-fic volume and better geometric characteristics (high quality, less curvature)which makes them less prone to accident occurrence. The length of toll roadshas a stepwise increasing trend during the period under study, with an averageannual increase rate of 3.49%.

2.2.6 Legislative measures

Considering the significant impact of the driver behavior on traffic accidentsthe institutions involved in traffic safety recommend a number of the measureshave to be taken by the authorities. These measures include penalty pointsystems which refers to the suspension or the revocation of the right to drive.The direct effect of these enforcement laws does not only depend on the mereexistence of the legislation but also how strictly they are enforced. In therecent years there have been mainly two regulatory measures taken by theSpanish authorities in order to improve road safety:Penalty Point System(PPS) and Penal Code Reform (RPC) (Figure 2.9). In addition to theenforcement laws, the DGT has been involved in different publicity campaignsand adds promoting traffic safety through the media, that were representedby safety items covered in the press, RUIDO, in this study. RUIDO is thenumber of news items or references to road safety in the national press as anindicator of the presence or intensity in all kinds of news media. It can beobserved that RUIDO has a smoothly increasing trend till 2004 that startsto sharpen after this period (Figure 2.9). On average RUIDO has increased50.16% per year during 2000-2009.

2.2.6.1 Penalty Point System

PPS was enforced on July 1st , 2006 (Boletın Oficial del Estado numero:172/2005; 28/2006) with the goal to re-educate and penalize the persistent


2.9.a

2.9.b

2.9.c

Fig. 2.9. Legislative measures.

2.9.a)PPS; 2.9.b)RPC; 2.9.c)RUIDO.


offenders by a reduction or loss of the 12 credit points given to the driverssince the time the law came into force. The loss of points in this case hap-pens due to exceeding the speed limit, carrying out high risk maneuvers, anddriving under the influence of alcohol or other prohibited substances. ThePPS has been implemented in different countries, among them United King-dom (1972), Germany (1974), France (1992), Austria (1993), Poland (1993),Greece (1993), Ireland (2002), Italy (2003). To estimate the effect of the PPSon traffic safety, a number of studies have been carried out. These studies canbe grouped into 3 categories: studies on effectiveness of the system, studies onhealth issues, and studies on driver behavior changes (Aparicio et al. , 2011).The effect of the PPS in Spain has been studied by Aparicio et al. (2011),Castillo-Manzano et al. (2010), Pulido et al. (2009). Pulido et al. (2009)find out that during the period 2000-2007 the number of fatalities have fallenby 14.5%. Castillo-Manzano et al. (2010) analyze the effect of the PPS onthe safety indicators such as number of deaths and injured during the 24 hoursin highway and built-up areas in. Studying the time period of 1980-2007 theyconclude that the PPS has caused 12.6% reduction in the number of deathsin highway accidents. The study shows that the introduction of the PPShas also caused a decrease in the number of injuries in highway accidents andin built up areas by 15.3% and 17.2% respectively, however this effect fadedaway in the following year after the law came into force. Aparicio et al.(2011) study the effect of the PPS on the road safety measures. Studyingthe time period of 1995-2009, it was found out that introduction of PPShas caused 11.27-13.9% reduction in the number of fatalities during 24 hours.Apart from this effect the PPS had an immediate impact on the number offatalities during the summer months following the introduction of the systemwhich was maintained over the following summers.

2.2.6.2 Penal Code Reform

RPC was enforced December 2nd, 2007 (Boletın Oficial del Estado numero:288/2007). The RPC is depicting the harsher measures taken by the gov-ernment for the road safety offences. According to the law certain trafficoffences such as driving at a speed of 60 km/h over the legal speed limit inurban roads and 80 km/h on urban roads, driving under the influence of toxicdrugs, narcotic, psychotropic substance or alcohol beverages (over 1.2 gr/l)were regarded as a criminal offence from then on and can be penalized withprison sentence, fines and community work. The RPC effect was studied byAparicio et al. (2011), Castillo-Manzano et al. (2011). Aparicio et al.


(2011) found out that the RPC had a positive effect on reducing the numberof fatalities starting from November 2007, a month before the law came intoforce, which they explain with the media impact and social debate that wasobserved prior to the enactment of the law. It is shown that there was a 17.7-20.7 % reduction in the number of fatalities over 24 hours in the followingfirst year. Castillo-Manzano et al. (2011) evaluate the impact of the RPC onroad traffic fatalities during 24 hours and try to forecast the time that effectwould last. They also conclude that the RPC had decreased the road trafficfatalities starting from November 2007. Between November 2007 and Decem-ber 2007 the fatality rate was reduced by 534 (24.7%). During the following13 months the reduction stayed at a constant 16% and the study concludesthat this effect seemed to be more persistent than PPS enforcement.

2.2.7 Weather conditions

Among the factors affecting the crashes and the severity level of the accidentsthere are also weather conditions. A significant variation observed in numberof accidents and severity level of it depending on the level of precipitation andthe season, because driving exposure changes by these factors. The influenceof the climate conditions on road safety has been studied mainly in two direc-tions: the effect of the temperature and the effect of the precipitation (rainfallor snow). The results of these studies can be generalized as follows: highertemperature (summer months) and rainfall are associated with increasing ac-cident risk specially in the case of fatal accidents (Andreescu and Frost , 1998,Bertness , 1980, Brodsky and Hakkert , 1988, Fridstrøm et al. , 1995, Sternand Zehavi , 1990), while the fatal accident risk reaches its minimum duringthe winter months and the snowfall (Brijs , 2008, Eisenberg , 2004, Farmerand Williams , 2005, Fridstrøm et al. , 1995). These findings are explained bythe fact that exposure increases during the summer period and on the otherhand it decreases during the winter period, particularly during the snowfall.

The weather conditions are represented by precipitation and tempera-ture variables. The precipitation is represented by the amount of rainfall(PREC), number of snowing days (DNIE), number of foggy days (DNIEB),and number of days with snow-covered ground (SLNV ). The temperature isrepresented by the amount of sunny hours (HSOL), and average temperature(TEMP ) (Figure 2.10). Weather variables were averaged first with 42 mete-orological stations covering 11 regions and then the weighted average for thewhole country was computed. PREC fluctuates between 10-130 mm, withan average value of 50 mm. On average DNIE is at most 3 and at least 0


2.10.a

2.10.b

2.10.c


2.10.d

2.10.e

2.10.f

Fig. 2.10. Weather conditions.

2.10.a)PREC; 2.10.b)DNIE; 2.10.c)DNIEB; 2.10.d)SLNV ; 2.10.e)HSOL;

2.10.f)TEMP .


(days) during a single month. These values for DNIEB are 7 and 1 (days)respectively. The average temperature, TEMP , fluctuates around 6-26 ◦C,while the average amount of sunny hours, HSOL, changes between 103-343hours.

2.2.8 Calendar effect

Calendar effects are represented by the number of weekdays (DLAB), num-ber of weekends and holidays (SDF ) and Easter break (SEMSAN) (Figure2.11). All of the variables were averaged for the whole country. The calendareffect variables (SDF and SEMSAN) have been shown to have a negativeeffect on road safety, since during the weekends, holidays and Easter breakthe travel volume increases (Liu and Sharma , 2006), thus increasing the acci-dent rate (Fridstrøm , 1999, Garcıa-Ferrer et al. , 2006, Gaudry and Lassarre, 2000).

2.3 Adjusting the data: missing values

The missing values of the variables that were absent in the data due to thedelay in the collection and recording process were obtained by forecastingthrough ARIMA models. For this purpose the automatic forecasting proce-dure provided by TRAMO/SEATS software (Maravall and Gomez , 1996)was applied. TRAMO stands for ”Time series Regression with ARIMAnoise, Missing values and Outliers” and SEATS for ”Signal Extraction inARIMA Time Series”. TRAMO is a program for estimating and forecast-ing regression models with possibly non-stationary (ARIMA) errors and anysequence of missing values. It detects several types of outliers as well asTrading Day and Easter effects which are modeled through intervention vari-ables. TRAMO pre-adjusts the series that is going to be subsequently fittedby SEATS. The missing value treatment was carried out for the followingvariables: PARO, CONALC, RADAR, PRADAR, SUSP , PRLSUSP ,V EH10 and RUIDO.

2.4 Summary

In this chapter the data used in this study are presented. The dependentvariables represent the road safety indicators in Spain that will be further

41 2.4. Summary

2.11.a

2.11.b

2.11.c

Fig. 2.11. Calendar effect.

2.8.a)DLAB; 2.8.b)SDF ; 2.8.c)SEMSAN .


analyzed in the next chapters. They consist of 2 sets of times series: 1) van-involved road accident frequency and severity; and 2) total fatal accidents.The first set of data cover the period of 2000-2009, while the second datawere studied for the period of 2000-2011. These indicators will be studiedas the function of independent variables. The independent variables in turnare divided into several categories, such as exposure, economic factors, drivercharacteristics and surveillance, vehicle characteristics, road infrastructure,legislative measures, weather conditions and calendar effects. The behaviorof each independent variable is separately analyzed through the indicatedperiod.

Part II

Computational Tools for the

Evaluation and Analysis of

Road Safety.

43

Overview

As indicated in the Part I, the objectives of the thesis are the analysis of theroad safety indicators in Spain. For this purpose two data sets, representingthe current problems in road safety in Spain are analyzed. The analysis arecarried out through econometric models, to be presented in chapter 3. Themethodological contribution of the thesis is mainly divided into three partsand presented in three different chapters as presented below.

• Chapter 4: This study is intended to analyze the main factors explainingvan accident behavior during the period 2000-2009 and to get a furtherinsight into dynamic macro models for road accidents. For this purposefour time series related to the frequency and severity of van accidentson Spanish roads were considered. The estimation and prediction werecarried out for two different macro models, DRAG, and UCM. Since thechoice of the appropriate macro model for the analysis of road traffic ac-cidents is not a trivial matter, we are considering multiple factors such asgoodness of fit and interpretation, as well as the prediction accuracy inorder to choose the best model. Apart from explaining the van-involvedroad accident indicators, the main contribution of this chapter was themacro model comparison for the road safety analysis. The choice ofthe methodological approach for the analysis of road safety indicatorsis still an ongoing study. Therefore a special attention was given tothe differences between the results provided by different methodologies.Overall, the final results agree with the literature as far as the statis-tical fit measures were concerned. It was found that the DRAG- typemodel yields slightly better predictions for all four models compared toUCM. With these macroeconomic models, the effect of some influentialfactors (fleet, drivers, exposure variables, economic factors, as well aslegislative actions) can be addressed. Estimating the effect of the vigi-lance and surveillance actions can help safety authorities in their policyevaluation and in the allocation of resources.

45

46

• Chapter 5: The main objective of this chapter was the analysis of num-ber of fatal accidents in Spain, during 2000-2011 and determining themain factors that had a significant effect. Determining the main fac-tors affecting the behavior of number of fatal accidents is main questionof this chapter. Macro model selection exercise is considered to be alengthy and most of the time biased process, specially if the modelselection is based on the user defined fit statistics, such as p−values.In this case the choice of fully specified models versus parsimoniousmodels needs a special consideration. Taking these issues observedin road safety literature into account a model selection methodologyis proposed. Considering the results of chapter 4 the methodology iscarried out using a DRAG like parsimonious SE model, where the es-timation was carried out within the Bayesian framework and basedon MCMC methods. The model selection procedure was later cross-validated through prediction analysis and the results were comparedwith fully specified DR model. The results of the model selection pro-cedure showed that the economic factors, legislative measures and roadinfrastructure have more significant effect on the number of fatal acci-dents during the period under study.

• Chapter 6: The main objective of the chapter was to analyze howthe parameters of a selected model capture the parameters of the truemodel. The methodology is based on application of factorial design andANOVA techniques, to compare two of the most relevant time seriesmodels used for traffic data. Study was carried out using simulateddata, hence the name simulation experiment based methodology wasgiven. Taking into account the results of chapter 5, a special attentionwas given to the modeling of stochastic component that might be ex-istent in the true data, through a stationary model like DRAG or SE.The UCM includes a specific stochastic trend component that can beseparately modelled. Thus considering the empirical study carried outin chapter 4, this work was carried out using DRAG and UCM, henceto generate a new data the results of the indicated study was used. Inorder to generate a stochastic process, the data was simulated using ad-ditional trend component. The ”true” data was thus generated throughUCM methodology, and a DRAG model was estimated using the gen-erated data. The results of the research shows that although the trueeffects of the variables are captured in the DRAG model, a stochasticcomponent can have a significant impact on regression elasticities thuson the interpretation of model.

Chapter 3

Statistical methodology

This chapter is dedicated to the macro models for the analysis of road safetymeasures. In the section 3.1 model functional forms and their application inroad safety literature are presented. In section 3.2 model estimation method-ology and the goodness of fit measures are discussed. Sections 3.3 and 3.4are dedicated to variable analysis, i.e. elasticity- interpretation of variableimpact and multicollinearity- the collinearity observed between two or morevariables.

3.1 Functional form

3.1.1 Dynamic regression

Dynamic regression (DR) states how an output, Yt, is linearly related tocurrent and past values of the inputs, Xkt (Pankratz , 2012), i.e.:

Yt = β0Xt + β1Xt−1 + β2Xt−2 + ...+ ut (3.1)

where the coefficients, β0, β1..., represent the dynamic relationship betweenthe series Yt and Xt. Equation (3.1) is referred as the transfer function. Thisequation can be re-written using the lag operator, B, in the following form:

Yt = β(B)Xt + ut (3.2)

where

β(B) = β0 + β1B + β2B2 + ... (3.3)

47

Chapter 3. Statistical methodology 48

which can be represented as the polynomial in lag operator through:

β(B) =ω(B)

δ(B)(3.4)

If both series, Yt and Xt, are stationary, then the error term, ut willfollow an autoregressive moving average (ARMA) process defined as:

φ(B)ut = θ(B)wt (3.5)

where wt is assumed to be a white noise. This model based on equations (3.1)-(3.5) is known as DR or transfer function model between the two variables.

In order to estimate DR model, equations (3.1)-(3.5) are simplified intothe following form:

Yt =ω(B)

δ(B)Xt +

θ(B)

φ(B)wt (3.6)

The general form of equation (3.4), where the integration of variables isnecessary, is as follows:

Yt =ω(B)

δ(B)Xt +

θ(B)Θ(Bs)

φ(B)Φ(Bs)∇∇swt (3.7)

where ∇ and ∇s represent the regular and seasonal integration respectivelyof the series Yt and Xt, and the error term has regular and seasonal ARparameters φ(B) and Φ(Bs) and regular and seasonal MA parameters θ(B)and Θ(Bs). The DR models are described in more detail in Pena (2005) andPankratz (2012).

3.1.1.1 Structural explanatory models

One special case of DR model that will be used in this thesis is the structuralexplanatory (SE) model. The SE model is based on linear regression withautoregressive errors. The earlier version of these type of models was studiedby Zellner and Tiao (1965) and Zellner (1971). The model with AR(2) errorstructure, studied by Zellner (1971) has the following functional form:

Yt =∑k

βkXkt + ut (3.8)

(3.9)

49 3.1. Functional form

ut = ρ1ut−1 + ρ2ut−2 + wt (3.10)

where Yt is the dependent variable, usually a road safety indicator; Xkt rep-resents different factors that are assumed to have an impact on safety; βk arethe regression coefficients; ut is an error term with the AR(2) structure; andwt are assumed to be white noise IID with N(0, σ2

w).

3.1.2 Demand for Road use, Accidents and their Grav-

ity (DRAG)

The functional form of DRAG modeling is specified as the following regressionmodel (Liem et al. , 2008):

Yt =∑k

βkXkt + ut (3.11)

ut =[exp

(δm · Z

(λZm )mt

)]1/2· vt (3.12)

vt =∑l

ρlvt−l + wt (3.13)

where Yt is the dependent variable, usually a road safety indicator, and Xkt

represents different factors that are assumed to have an impact on the safety.the error structure includes heteroskedasticity term, Zmt, with coefficient δmand is assumed to follow an AR(l) process. The first-stage vector of residuals,ut are heteroskedastic; the second-stage residuals, vt are autocorrelated andthe third-stage residuals, wt are assumed to be IID, with normal distributionN(0, σ2

w). All model variables, Yt, Xkt, and Zmt are Box-Cox transformed(Box and Cox , 1964).

3.1.2.1 Box-Cox transformation

Usually in traffic accident analysis count data are most frequent. However,continuous data models are preferred because they consider the autocorre-lated structure of time series and can be handled easily by considering theunobserved components. Thus the modeling of count data using continuousdata models has become a common exercise in road safety analysis. One wayof doing this is using the Box-Cox family of power transformations (Box and


Table 3.1: DRAG family models.

Country Authors Monthly period Model

Germany Blum and Gaudry 1968-1989 SNUS

France Jaeger and Lassarre 1957-1993 TAG

Norway Fridstrøm 1973-1994 TRULS

Sweden Tegner 1970-1995 DRAG-Stockholm

California McCarthy 1981-1989 TRACS-CA

Spain Aparicio et al. 1990-2004 DRAG I-DE Spain

Algeria Gaudry and Himouri 1970-2007 DRAG-ALZ-1

Cox , 1964), which helps to achieve normality and a linear growth function.The predictive accuracy has also been shown to improve substantially whenthe model variables are Box-Cox transformed (Keramidas and Lee , 1990,Lee et al. , 1987). The Box-Cox transformation (BCT) lets the data deter-mine the most appropriate functional form under which the variables shouldappear:

Y(λY )t =

{YλYt −1λY

, if λ 6= 0

ln(Yt), if λ = 0(3.14)

where λY is the transformation coefficient.

3.1.2.2 DRAG family models

Based on the original DRAG model for Quebec, a family of DRAG-inspiredmodels were developed for another countries and regions (Table 3.1 ). Thelist of the DRAG family models and their main characteristics is discussedbelow.

• SNUS (Straßenverkehrs-Nachfrage, Unfalle und ihre Schwere) was de-veloped by Blum and Gaudry (2000) covering West Germany. Theestimation period for this model was 1968-1989. The main particu-larity of this model is the inclusion of the material damage accidents,considering both light and severe damages. Also two separate modelsfor diesel and fuel vehicles were constructed.

For the SNUS model some specific issues characteristic to case of Ger-many had to be taken into account: the absence of speed limit, impor-tant car industry, and the turning points observed in the data, causedby the unification of the country.


As to the results of the study, the material damage was found to beincreasing by the influence of exposure, high temperatures, seat belt useand shopping habits. The severity of the road accidents were found tobe increasing by exposure, higher temperatures and beer consumption.Increasing fuel prices and introduction of speed limits seemed to havea positive impact on the safety indicators.

• TAG (Transport routiers, Accidents et Gravite) was developed by Jaegerand Lassarre (2000) for France. The estimation period for the TAGmodel was 1957-1993. The model consists of four layers: risk exposure(kilometers traveled), the risk behavior (average speed), injury accidentfrequency and accident gravity. There were fifty explanatory variablesintroduced to all four models. The risk exposure was found to be posi-tively related with the employment index, wine consumption per adult,stock of private cars and the average temperature. The risk exposureon the other hand decreases by the impact of the technical inspectionof vehicle and increase in fuel prices. The risk behavior was found tobe increasing as the motor vehicle price index and percentage of theprivate motor cars increases. Also the seat belt use was found to havea positive effect on the risk behavior. The legislative measures and fuelprices were found to reduce the average speed. The factors such as av-erage speed, number of motorcycles, the total kilometers traveled, wineconsumption and the industrial activity increase the accident frequencyand gravity, while the road safety measure were essential in decreasingthese road safety indicators. Also temporary factors, like the Gulf war(consequently increasing fuel prices) had a positive impact on decreasingthe accident frequency.

• TRULS (TRaffik, Ulykker og deres Skadegrad) was developed by Frid-strøm (2000) for Norway, covering the period 1973-1994. Unlike theother DRAG family models , Fridstrøm assumes a Poisson distributionfor the causality counts. The model includes additional econometricmodels explaining the seat belt laws and car ownership. Further a layerof light and heavy road use are included and the results are disaggre-gated by road users categories (pedestrians, cyclists, motorcyclists andcar drivers). The main results of the TRULS model are summarized asfollows: the injury accidents increase in proportion to the traffic vol-ume, also the use of heavy vehicles increases the injury accidents. Thesnowfall has an increasing effect on the injury accidents, however theseverity of the accidents diminishes. Moreover there are less injury acci-


dents when the ground is covered by snow. Rainfall also has decreasingeffect, this is partially explained by the fact that on the rainy days theexposure of unprotected road user (pedestrians, cyclists) is reduced.During the first quarter of pregnancy the frequency of injury accidentsare increasing. The severity of the accidents is reduced by wearing theseat belts and temperature falling below zero. The severity increase bythe alcohol consumption. As to the car ownership, it is shown that itincreases ceteris paribus with the size of population and the increase inhousehold income.

• DRAG-Stockholm model for Stockholm was developed by Tegner andLoncar-Lucassi (1997), covering the time period 1970-1995. The modelestimates three road safety indicators: the exposure, accident frequencyand accident severity. This model has many U-shaped effects, suchas the effect of vehicle-kilometers, volume of heavy vehicles and moremotorways. Although these factors contribute to worsening of safety onthe roads, after the congestion occurs they have a decreasing effect onthe dependent variables. Another U-shaped effect was found betweenalcohol and medicine consumption and number of injury accidents. Atlow consumption levels the accident risk is reduced , however when theconsumption increases the risk augments rapidly. Additionally the seatbelt usage reduces the number of injury accidents and impact of theheadlight use during daytime increases the number of fatalities.

• TRACS-CA model was developed by McCarthy (2000) for Califor-nia, covering the period of 1981-1989. The model estimates accidentfrequency and severity including with the material damage accidents.The three main components are risk exposure, accident frequency (fa-tal, injury, material damage) and accident severity (number of deathsand injuries). The predictors are grouped into three categories: socio-economic, transport system, and environmental factors. The results ofthe study show that the exposure increases with beer consumption andincreased speed limit. The factors such as risk exposure and consump-tion of beer are positively related to fatal crashes, while the rainfall andlegislative measures have a decreasing effect. The injury crashes increasewith the wine consumption, rainfall, increased speed limit and seat beltuse , while the latter has risk substitution effect, i.e. when crash occursless people are injured. The injury related crashes decrease with the in-creasing fuel prices. As to the material damage accidents, it was foundto be reducing as fuel prices increase and increasing with the exposure


and increased enforcement law. The reason for the latter needs furtherinvestigation.

• DRAG-Spain was developed by Aparicio et al. (2013) for Spain. Theestimation was done for the period of 1990-2004 and was applied to thenetwork of interurban roads. DRAG-Spain model is a three layer modelthat includes the exposure, accident frequency and accident severity.The data included in the model contained monthly, quarterly and an-nual data. The quarterly and annual was disaggregated using indicatorvariables. The missing variables were obtained by extrapolation. Theanalysis show that most significant factor is exposure, which togetherwith inexperienced drivers, speed and the aging vehicle stock, have anegative effect on the road safety and were found to be increasing thesafety indicators, while an increase in road surveillance and techno-logical improvements to vehicles were found to have decreasing effecton both accident frequency and accident severity. Additionally the ef-fects of other factors such as climatology and labor conditions wereestimated. Like the TRULS model it was shown that during the dayswhen the ground is covered with the snow the frequency of accidentsincrease but the severity decreases. The rainfall had a similar effect.While high temperatures increase the frequency and the severity of theaccidents. The number of weekend and holidays was also found to havea negative impact on road safety.

• DRAG-ALZ-1 is the latest DRAG family model. It was developed byGaudry and Himouri (2013) for Algeria. The model covers the period of1975-2007. It is a three layer model (exposure, accident frequency andseverity, victims ). The model includes additionally subsidiary equa-tions for speed and seat belt wearing. The results of the study indicatethat the use of heavy vehicles increase the frequency of the accidents butreduce the severity. Higher temperature and more daylight increases theexposure and the speed, consequently increasing fatal accidents. Thelegislation showed to have positive effect on road safety, decreasing bothfrequency and severity of the accidents. The fuel prices did not seem tohave significant effect on road safety indicators. This was explained bythe fact that the price of fuel is very cheap compared to other countriesincluded in the previous DRAG models. The economic activity, as itwas expected increases the exposure and consequently the frequencyand severity of the accidents, while the unemployment decreases the fa-tal accidents and the number of deaths. During the special events, such


as religious holidays, the number of accidents and the severity increasesbut the effect is very weak.

3.1.3 Unobserved Components Model (UCM)

The stochastic framework for UCM is based on state-space methodologywhere the measurement equation incorporates unobserved components suchas trend and seasonal patterns (Harvey and Durbin , 1986):

Yt = µt + γt + εt (3.15)

where µt represents the trend, γt the seasonal component and εt the irregulardisturbance term. The measurement equation can be extended to include theexplanatory and intervention variables.

The parameter and component estimation is based on Kalman filtering.The measurement equation decomposes the observed time series into unob-served deterministic or stochastic components that are modeled separatelyusing state equations:

µt = µt−1 + βt−1 + ηt (3.16)

where βt is slope:βt = βt−1 + ζt (3.17)

and ηt and ζt are error terms, that are normally distributed as ηt ∼ N(0, σ2ηt)

and ζt ∼ N(0, σ2ζt

) respectively. By setting σ2ζt

= 0 the model becomes a lineartrend with a fixed slope, while setting σ2

ηt = 0 will result in a smoother trend.The model becomes a deterministic linear time trend if both the variances(σ2

ζt= σ2

ηt = 0) are zero, µt = µ0 + β0 · t.The seasonal component is capturing the fluctuations in the time series

data and is handled by a trigonometric function:

γt+1 =s−1∑m=1

γt+1−m + ωt (3.18)

where s represent the integer period for which the sum,∑s−1

m=1 γt−m, is zero inthe mean. The error terms ωt are i.i.d., ωt ∼ N(0, σ2). The cycles ψt,j have

frequencies ωj =2πjs

and are specified by the following matrix:[ψt,jψ∗t,j

]=

[cosψj sinψj− sinψj cosψj

] [ψt−1,jψ∗t−1,j

]+

[ωt,jω∗t,j

](3.19)

where ωt,j and ω∗t,j are assumed to be independent.

55 3.2. Model estimation and diagnosis

In this thesis we consider the UCM that will be estimated by adding theexplanatory and intervention variables to the measurement equation (3.15):

Yt = µt + γt +J∑j=1

δjXjt + ωt + εt (3.20)

where Xjt is the value of the jth explanatory variable at time t, and δj is thecoefficient. The ωt is the intervention variable defined as a dummy variable:

ωt =

{0, if t < τ1, if t ≥ τ

(3.21)

where τ indicates the time point when the change was made.

3.2 Model estimation and diagnosis

For model estimation maximum likelihood and Markov Chain Monte Carlomethods were applied. The estimation procedure for each type of model isdiscussed below.

3.2.1 Maximum likelihood estimation

Both DRAG and UC models are estimated using ML estimation. The MLestimation is based on the optimization of a given log likelihood function withrespect to the model parameters.

3.2.1.1 DRAG model

Assume the model (3.11)- 3.13) is simplified in a matrix form:

Y∗∗ = βX∗∗ + w (3.22)

The estimates of model parameters are then obtained through:

β =(X∗∗

′X∗∗

)−1X∗∗

′Y∗∗ (3.23)

σ2w =

1

N

(Y∗∗ − βX

∗∗)′ (Y∗∗ − βX

∗∗)


where

Y ∗∗t = Y ∗t −∑l

ρlY∗t (3.24)

X∗∗kt = X∗kt −∑l

ρlX∗t

When the heterosckedasticity term is allowed then Y ∗t and X∗kt are de-fined as:

Y ∗t = Y(λY )t /f(Zt)

1/2 (3.25)

X∗t = X(λX)t /f(Zt)

1/2

where Y(λY )t and X

(λX)kt are Box-Cox transformed.

The estimates are used to obtain the concentrated log-likelihood functionas:

L(θMLESE ) = −N

2[1 + ln(2π)]− N

2ln σ2

w −1

2

∑t

ln f(Zt) + (λy − 1)∑t

lnYt

(3.26)which is the function of model parameters, θMLE

SE = (λx, λy, λz, δ, ρ). Themaximization of the concentrated likelihood function with respect to modelparameters is based on the Davidon-Fletcher-Powell (DFP) algorithm, whichallows for the simultaneous maximization of all the parameters. The DFPalgorithm is similar to Newton-Raphson’s, but it does not require the analyticcalculations of second derivatives and approximates them iteratively.

3.2.1.2 UC model

Assume the model (3.15)-(3.16) has the following vector autoregressive (VAR)form:

Yt = AYt−1 + Ut (3.27)

The likelihood function for UCM is then constructed as:

L(θMLEUCM) =

∏t

f(Yt|Yt−1, θMLEUCM) (3.28)

where f(·) is normal density function:

f(Yt|Yt−1, θMLEUCM) =

1√(2π)n|Σε +HΣµ

t|t−1H′|

exp

(−u′t(Σε +HΣµ

t|t−1H′)−1ut

2

)(3.29)


where Σ(·) denotes the variance vector, and

Σµt|t−1 = BΣµ

t−1|t−1B′ + Ση (3.30)

A, B, and H are system matrices.The ML estimation of UCM is based on Gradient-based methods, such

as Newton’s method.

3.2.2 Markov Chain Monte Carlo estimation

The SE model is estimated through Bayesian inference. In Bayesian estima-tion the prior beliefs on the observed data are updated by Bayes’ theorem toobtain the posterior information (Raftery , 1995):

π(θ | x) ∝ π(θ)l(x | θ) (3.31)

where π(θ) is the prior distribution and l(x|θ) is the likelihood function.The major limitation for the use of Bayesian approaches is the computa-

tion of the posterior distribution that requires integration of high-dimensionalfunctions when a larger set of parameters is included in the model. Thisproblem has been overcome by Markov Chain Monte Carlo (MCMC) meth-ods, which simulate direct samples from some complex distribution of inter-est (Gelfand and Smith , 1990). MCMC methods have their roots in theMetropolis algorithm (Metropolis et al. , 1953), developed by physicists tocompute complex integrals by expressing them as expectations for some dis-tribution and then estimate this expectation by drawing samples from thatdistribution.

One particular MCMC method, is the Gibbs sampler, originally devel-oped for image processing (Geman and Geman , 1984). The Gibbs sampleris an iterative MCMC method designed to draw samples from the intractablejoint distributions by sampling tractable full conditionals (Casella and George, 1992).

Considering the parameters θ = {θ1, θ2, ..., θn}, with joint distribution[θ1, θ2, ..., θn] and full conditional distributions [θ1|θ2, ..., θn] and [θn|θ1, ..., θn−1],the Gibbs sampler algorithm for obtaining the marginal distribution fromjoint distribution proceeds as follows:

1. Specify initial values, θ(0)1 , ..., θ

(0)n , and set i = 1.

2. Update:


(a) θ(i)1 from [θ1|θ(i−1)2 , ..., θ

(i−1)n ]

(b) θ(i)n from [θn|θ(i−1)1 , ..., θ

(i−1)n−1 ]

3. Set i = i+ 1, and go to 2.

After N iterations, the sample of θ(N)1 , ..., θ

(N)n is obtained. Under the

regularity conditions as M →∞, the sampled values converge in distributionto the relevant marginal and joint distribution, i.e. θ

(N)i → θj ∼ [θj] and

(θ(N)1 , ..., θ

(N)n )→ (θ1, ..., θn) ∼ [θ1, ..., θn].

Assume the structural model (3.11)-(3.13) where the prior distributionof the model parameters, θMCMC

SE = {β, ρ, σ2w}, is given as:

π(β, ρ, σ2w) = π(β|σ2

w)π(σ2w)π(ρ) (3.32)

The model parameters are assigned Jeffrey’s uninformative priors (Zell-ner , 1971):

β|σ2w ∼ Nk(β0, σ

2wB−10 ) (3.33)

σ2w ∼ IG

(ν02,δ02

)ρ ∝ Nl(ρ0,Φ

−10 )

i.e. a combination of multivariate normal for β, an inverted gamma for σ2w

and a multivariate normal for ρ, where β0, B0, ν0, δ0, ρ0, and Φ0 are thehyperparameters that are set to be a equal to a constant.

3.2.3 Goodness of fit measures

Goodness of fit measures are used in order to estimate how well the model fitsthe data. One of the ways of checking goodness of fit is computing the likeli-hood level of a model, that is, how well the model maximizes the likelihoodfunction. The following goodness of fit measures are used:

1. Akaike information criteria

2. Bayesian information criteria

3. Deviance information criteria

4. R2−like measures


3.2.3.1 Akaike information criteria

The Akaike Information Criterion (AIC) was developed by Akaike (1973)and is based on minimization of the Kullback-Leibler distance between themaximum likelihood estimate and the true value. This measure also usesthe log-likelihood, but adds a penalizing term associated with the numberof variables. It is well known that by adding variables, one can improve thefit of models. Thus, the AIC tries to balance the goodness-of-fit versus theinclusion of variables in the model. The AIC is computed as:

AIC = −2(ln(likelihood)) + 2K (3.34)

where likelihood is the probability of the data given a model and K is thenumber of free parameters in the model. A smaller AIC value means a betterfit.

3.2.3.2 Bayesian information criteria

Similar to the AIC, the BIC also employs a penalty term associated with thenumber of parameters (K) and the sample size (n). This measure is alsoknown as the Schwarz Information Criterion. It is computed as follows:

BIC = −2(ln(likelihood)) +K · ln(n) (3.35)

Again, smaller values mean a better fit.

3.2.3.3 Deviance information criteria

Deviance information criterion (DIC) is the Bayesian version of the AIC andwas first proposed by Spiegelhalter et al. (2002). They assume the followingprinciple for Bayesian model comparison:

DIC = goodness of fit+complexity (3.36)

Goodness of fit is measured via the deviance. For a likelihood l(Y |θ )the posterior mean of deviance is defined as :

D (θ) = −2 log l(Y |θ ) (3.37)

Complexity is measured by the estimate of the effective number of pa-rameters:

pD = Eθ|Y [D]−D(Eθ|Y [θ])

= D −D(θ) (3.38)


i.e. posterior mean deviance, D, minus deviance evaluated at the posteriormean, D(θ). Then DIC is defined as :

DIC = D (θ) + pD =

= D (θ) + D −D(θ)

= 2D −D(θ) (3.39)

The model that provides the best predictions will have the lowest DICvalue. DIC values can only be compared between models that were builtusing the same set of information (Mitra and Washington , 2007).

3.2.3.4 R2−like measures

When the dependent variable is power-transformed, the R2 value using theordinary least squares linear regression is not available. In this case as good-ness of fit measure, Pearson’s R2 are considered (Liem et al. , 2008). This fitmeasure will be used for SE and DRAG models, where both dependent andindependent variables are power-transformed.

R2: computed with the expected value of Yt, E(Yt).

R2 =

[∑t

(Yt − E(Yt))(Yt − E(Yt))

]2∑t

(Yt − E(Yt))2∑

t

(Yt − E(Yt)

)2 (3.40)

where Yt are the estimated values of the dependent variable:

Yt =

{Y

(λY )t · λY + 1 if λY 6= 0

exp(Y(λY )t ) if λY = 0

(3.41)

And Y(λY )t are power transformed estimates of the dependent variable com-

puted as:

Y(λY )t =

∑k

βkX(λX)kt +

∑l

ρl

[Y

(λY )t−l −

∑k

βkX(λX)k,t−l

](3.42)

βk and ρl are the estimates of regression coefficients and autoregressive pa-rameters.

61 3.3. Elasticity estimation

3.3 Elasticity estimation

In order to estimate the sensitivity of a dependent variable Y with respect tochanges in independent variable Xk, the elasticities are taken into account.Elasticity is the ratio of the percentage change in independent variable, Xk

to the percentage change in dependent variable, Y . The elasticity of Y withrespect to Xk is computed as

ηYXk =∂E(Yt)

∂Xkt

· Xkt

E(Yt)= βk ·

Xkt

E(Yt)(3.43)

That is a 1% increase in Xk results a ηYXk% increase in Y .

Table 3.2: Elasticity estimates for different functional forms (McCarthy ,

2001).

Model Elasticity

Linear βk

(XktE(Yt)

)Log-linear βk (Xkt)

Linear-log βk

(1

E(Yt)

)Double log βk

The elasticities of the SE and DRAG models are computed as follows(equation (3.43)):

ηYXk =∂E(Yt)

∂Xkt

· Xkt

E(Yt)= βk ·

XλXkt

Y λYt

(3.44)

since the model variables are transformed.In the DRAG model the intervention variables representing regressors

such as enforcement laws are introduced to the model as a dummy whichtakes values 0 and 1. For the computation purposes these variables are notsubject to BCT thus the elasticity for the intervention variable is:

ηYXk =∂E(Yt)

∂Xkt

· Xkt

E(Yt)= βk ·

Xkt

Y λYt

(3.45)

Since the UC model estimation is carried out using the natural loga-rithms of the continuous variables, the regressor estimates of UCM can beinterpreted as the elasticities, i.e.:


ηYXk =∂E(Yt)

∂Xkt

· Xkt

E(Yt)=d log(E(Yt))

d log(Xkt)= βk (3.46)

3.4 Multicollinearity

To estimate the multicollinearity among the variables the correlation matrixfor the independent and dependent variables, in terms of the original values,is computed before the maximization procedure. To detect multicollinearitythe spectral decomposition of X ′X is used (Judge et al. , 1986):

X ′X =k∑t=1

γipip′i (3.47)

where pi is the (K × 1) eigenvector associated with the i−th eigenvalue γiof X ′X. Following the approach by Belsley (1980) the condition number of

a matrix, ηi = (γmax/γi)1/2 , is used in order to detect the near dependen-

cies among the columns of X. To assess the significance of the independentvariables, normal and conditional t-statistics are computed.

Another method for detecting multicollinearity is the estimation of vari-ance inflation factor (VIF), which is calculated as follows:

V IF (βk) =1

1−R2k

(3.48)

where (1−R2k) is the tolerance and is calculated as a function of the coefficient

estimate variance:

1−R2k =

σ2

n− 1· 1

V AR(Xkt)V AR(βk)(3.49)

Most commonly, a value of 10 has been recommended as the maximumlevel of VIF (Neter et al. , 1989).

3.5 Summary

In this chapter the dynamic statistical models used for the time series roadaccident data were presented. The application of this class of models inmodeling of road safety measures is mainly based on the fact that these typeof the models take the autocorrelated errors into account, that is observed in

63 3.5. Summary

the time series. In this thesis three main categories of models are considered:SE, DRAG and UCM models. The first two models estimate the accidentdata as the function of explanatory variables, considering an AR(l) structureof errors. In case of DR models, the error structure can be extended to followan ARIMA process. The third type of models estimate the accident data byseparating it into unobserved components such as trend and seasonality. Itis assumed that separating the data into these components the data filtersout autocorrelation observed in the series. The application and estimation ofcontinuous models on road safety will be discussed in details in Chapters 4-5.

Chapter 4

Explanation of van-involved

road accident indicators. Model

comparison

4.1 Introduction

The objective of this chapter is twofold: firstly, to select a model for theaccidental behavior of vans (see Section 2.1.2) with significant parameter es-timates that complies with the existing literature on road safety and presentsbetter prediction accuracy. Secondly, to get an insight into comparative mod-eling with two frequently applied dynamic models, DRAG and UCM.

Two macro models are considered for the analysis of van-involved ac-cidents: UCM (Section 3.1.3) and DRAG (Section 3.1.2) model. The twomodels are compared based on goodness-of-fit measures and prediction ac-curacy. The main difference between UCM and DRAG is the specificationand separate modeling of unobserved components, i.e. trend and seasonalcomponents, in the case of UCM. In the road safety literature the UCM arepreferred over classical, non-linear regression and DRAG models because asmentioned above, they can be used to explicitly decompose a time series intointeresting components such as trend and seasonal effect. They are also flex-ible and well able to handle the dependencies in time series. Furthermore,they work transparently with missing data and are easily generalized to themultivariate analysis of time series, while the DRAG model is simpler andhas a more straightforward interpretation. There is a very close relationship

65

Chapter 4. Explanation of van-involved road accident indicators. Modelcomparison 66

between UCM and ARIMA models, in such a way that one can almost al-ways find, given a specific model of any type, an equivalent in the other one.There is important literature on this issue (Harvey and Scott , 1994, Hillmerand Tiao , 1982, Maravall , 1985). However, in practice, DRAG, which isestimated using the TRIO package Gaudry et al. (2005), does not coverall the ARIMA model range since its stationary autocorrelation modeling isrestricted to AR structures.

In the following section the model estimation and selection process aregiven in detail. In Section 4.2 and 4.3 the data used in the chapter arediscussed. In Section 4.4 the model construction and estimation are presented.In Sections 4.5 and 4.6 the results of the model estimation and the predictionare analyzed. Finally, Section 4.7 the summary and the discussions of thischapter are presented.

4.2 Van-involved road accidents

Prior to the macro modeling of the safety measures involving vans, the fourtime series were decomposed into different components for the trend andseasonality check of the series. The prior time series analysis were carriedout using an automatic procedure provided by TRAMO/SEATS (Maravalland Gomez , 1996). During the automatic adjustment by TRAMO/SEATS,each dependent variable was decomposed into seasonal, trend and irregularcomponents (Figure 4.1). All four models were transformed into their naturallogarithms and were adjusted using the ”airline model”. The results of thisautomatic procedure are set out in Table 4.2. As we can see from the graph,there is no evolution of the estimated seasonal factors and the procedure yieldszero residual seasonality and no outliers, but Easter and trading day effectswere detected. The absence of the seasonality can be due to the turning point

Table 4.1: Dependent variables.

Variables Definition

ACCMOR Number of fatal accidents

MORHERN Number of accidents with seriously injured victims

MUER Number of fatalities

HERGRA Number of injured victims

67 4.2. Van-involved road accidents

4.1.a)


4.1.b)

69 4.2. Van-involved road accidents

4.1.c)


4.1.d)

Fig. 4.1. Decomposition of series into trend-cycle and seasonal components with

TRAMO/SEATS:


71 4.3. Independent variables

Table 4.2: Summary of TRAMO/SEATS results∗.

Estimate ACCMOR MORHER MUER HERGRA

statistics

MA1 -0.9765 -0.5850 -0.9930 -0.6352

MA12 -0.9872 -0.9889 -0.9926 -0.8870

BIC -31.311 -47.297 -28.732 -41.523

SE(at) 0.1985 0.0908 0.2258 0.1211

N(at) 0.5787 0.6423 0.1385 2.221

Q24(at) 20.40 12.88 24.40 14.72

QS(at) 0 0 0 0

∗MA1 and MA12 are the moving average parameters; BIC-Bayesian Information

Criteria; SE(at)− standard error of the residuals, should be small; N(at) is the

Bowman-Shenton test of normality of residuals, which should be smaller than 6;

Q24(at) is the Ljung-Box test for residual autocorrelation; QS(at) is the test for

the residual seasonality autocorrelation.

effect that apparently took place almost in the middle of the series (aroundJuly 2006), which shifts the series mean thus causing misspecification of thetrue model. This effect can also be observed looking at the trend cycle graph.Although it was not statistically tested, we assume that this shift was dueto the introduction of the Penalty Point System (2.2.6.1) in July 2006. Butsomehow the shift in the trend was not detected as a level shift outlier. Thefurther macro analysis of road safety measures including the frequency andseverity of van-involved accidents are presented the next chapter.

4.3 Independent variables

The explanatory variables used as traffic safety factors were divided into thefollowing categories: exposure, economic factors, driver behavior and surveil-lance, fleet characteristics, road infrastructure, legislative measures, weatherconditions and calendar effect (Table 4.3).


Table 4.3: Explanatory variables, 2000-2009.

Variable Definition

Exposure

PRGFUR Van Fleet

VKM Vehicle Kilometers Travelled

CONOIL Diesel Consumption

COMTOT Fuel Consumption Total

Economic factors

IPI IPI

INDVEN Sales Index

INDCOM Commerce Index

MANT Maintenance Investment

CONST Construction Investment

PREC Fuel Price

INDACT Activity Index

PARO Total Unemployment

PARSER Unemployment Service Sector

Driver behavior surveillance

CONALC Random Alcohol Checks

RADAR Speed Controls

PRADAR Positives in Speed Controls

SUSP Driving License Suspended

PRLSUSP Driving License Suspended (B and B1 type)


AIRBAG Airbag Equipped,% of Total Fleet

ABS ABS Equipped, % of Total Fleet

Road infrastructure

LONRAC High Capacity Roads, % of Total Network

LONRED Length of Toll Roads


PPS Penalty Point System

RPC Penal Code Reform

RUIDO Safety Items in Press

Weather conditions

DNIE Number of Snowing Days

SLNV Number of Days with Snow Covered Ground

TEMP Average Temperature

Calendar effect

DLAB Working days

SDF Weekend and Holidays

73 4.4. Model construction and estimation

4.4 Model construction and estimation

The DRAG model for van accidents consists of 2 layers: accident frequency(fatal and seriously injured) and accident gravity (fatal and seriously injured).As mentioned above, for constructing the models using the DRAG methodol-ogy, the TRIO software was used (see Appendix I for TRIO outcomes). Themodel construction begins by estimating the power transformation (eitherdifferent or the same coefficients for dependent and independent variables)and the autoregressive order of the errors and then including the indepen-dent variables. In the case of the ACCMOR, MORHER and MUER models,the BCT parameter was the same within each model for all variables, bothdependent and independent. In the case of HERGRA, the BCT values forthe set of independent variables, on the one hand, and the dependent one, onthe other, were different. The intervention variables (RPC and PPS) and thevariables with zeros (SLNV and DNIE) were not power transformed. Afterdefining the BCT and AR structure as the basic parameters, the remainingestimation was carried out (Table 4.4). First the variables that were assumedto have an effect on traffic accidents were added to the model and estimated.The variables with less significant and less interpretable effects were elimi-nated and new models were estimated. It should be pointed out that, duringthis stage, the BCT value and AR structure of the model can be fitted again.This will depend on how significant the fit statistics are.

After this step, different models with better fit statistics and significantestimates were obtained. In order to select the final DRAG model, predictionaccuracy was computed for each, and the final one was selected based on thebest forecast. The fit statistics for the selected DRAG models are listed inTable 4.4.

108 observation points were used for estimation. The adjusted R2 for thenumber of fatal accidents, number of accidents with seriously injured victims,number of fatalities and number of injured victims were 0.463, 0.714, 0.440 and0.630 respectively.

The data used in the statistical analysis are monthly observations, thusthere is a 12th order autocorrelation. Since the Durbin-Watson test of auto-correlation assumes that there are no higher order correlations, it would beless useful for residual analysis than the log-likelihood test.

For the UCM analysis the data were transformed into natural logarithms.The UCMs were built using the SAS/ PROC UCM software (Selukar , 2011)(see Appendix II for SAS outcomes). The UCM estimation consists of twoparts. First the models were built using three descriptive- level, slope and sea-


Table 4.4: Parameter estimates of DRAG models.

BCT ACCMOR MORHER MUER HERGRA

coefficients

λY 0.168 0.067 -0.084 -0.019

λX1 0.168 0.067 -0.084 -0.373

λX2 -0.196

AR ACCMOR MORHER MUER HERGRA

coefficients

ρ1 -0.324 -0.485 0.103

ρ2 -0.275 0.058 -0.315 -0.020

ρ3 -0.128 0.061 -0.107 0.062

ρ4 -0.248 0.193 -0.210 0.150

ρ5 0.117 0.042

ρ6 0.037 0.198

ρ7 -0.043 -0.076

ρ8 0.138 0.189

ρ9 -0.095 -0.206

ρ10 -0.268 -0.261

ρ11 -0.035 -0.097

ρ12 -0.020

ρ14 -0.186 -0.206

Table 4.5: Fit statistics of DRAG models.

Fit statistics ACCMOR MORHER MUER HERGRA

Log-likelihood: -309.861 -368.933 -333.696 -409.788

Pseudo-R2:

-(E) 0.578 0.785 0.576 0.729

-(E) Adjusted 0.463 0 .714 0 .440 0 .630

Observations 108 108 108 108

75 4.4. Model construction and estimation

Table 4.6: Fit statistics of UCM components.

Fit statistics ACCMOR MORHER MUER HERGRA

Full Log-likelihood 24.806 83.078 73.494 -8.156

AIC -47.61 -164.2 -12.7 18.31

BIC -44.88 -161.5 -9.954 20.94

χ2Seasonal NP 29.6 NP 38.66

D.F. (11) (11)

Error variance, σ2γ 0 0 0 0.0151

sonal components and the intervention variables, then adding the explanatoryvariables that are assumed to have a significant effect on road safety (Hirstet al. , 2005). There are two steps to consider while including the descriptivecomponents in the model. The first step is to decide whether the componentis time varying and secondly whether it is contributing to the response vari-ability. The components can enter the model either stochastically (non- zerovariance) or deterministically (zero variance) and are included in the model ifsignificant. We require the p-value to be below 10% (Hermans et al. , 2006).Note that in order to choose the best UCM we have used fit statistics suchas AIC and BIC.

The results of the final descriptive models are listed in Table 4.6. In allfour UCM both the slope and level error variances were set to zero (σ2

η =σ2ξ = 0), meaning the models have a linear trend. The seasonal compo-

nent was absent in the ACCMOR and MUER models but was includedfor MORHER and HERGRA. In the MORHER model the seasonal com-ponent was introduced as a deterministic component, (χ2

Seasonal = 29.6),while in the case of the HERGRA model it enters as a stochastic compo-nent (χ2

Seasonal = 38.66;σ2γ = 0.0151). The intervention variables (PPS and

RPC) were removed from all the models, except for HERGRA, where onlyRPC was found to be significant (bRPC = −0.05).

As the final step in UCM building, the effects of the explanatory vari-ables were estimated: as in the case of DRAG models, first all the explana-tory variables that were assumed to have a significant effect on traffic acci-dent severity and frequency were included in the descriptive model and thenthe variables with non-significant estimates were eliminated using a stepwiseprocedure. Both dependent and independent variables are transformed intonatural logarithms. As before, a 10% significance level was considered as thevariable selection criteria. It was initially assumed that some of the explana-tory variables have a lagged effect on the accident risk and fatality, thus some


Table 4.7: Normality test of UCM errors.

Dependent Shapiro- Pr<W Kolmogorov Pr>D

variable Wilk Smirnov

ACCMOR 0.986167 0.4286 0.078734 >0.1500

MORHER 0.98172 0.2130 0.081657 0.1238

MUER 0.983705 0.2492 0.062932 >0.1500

HERGRA 0.982682 0.2493 0.124208 <0.0100

were introduced with and without their lagged values (Garcıa-Ferrer et al., 2006, 2007). After comparing the model fit statistics only CONALC wasincluded in ACCMOR and MUER with its lagged value. The best modelwas chosen according to the AIC statistics. It should be noted that, unlikeDRAG, where the performance and the goodness of fit of the model improveas more variables are added, the UC estimation procedure used here does notallow the inclusion of so many variables because of multicollinearity. In thecase of the UCM a better prediction was obtained when the model includedhighly significant estimates of the variables, which in turn yields better AICstatistics.

The residual analysis of UCM was carried out by checking the validity ofthe hypothesis of normality, homoscedasticity and independence of the errors(Figure 4.2). For normality, we have carried out graphic inspection (Figure4.2) and Kolmogorov- Smirnov and Shapiro-Wilk normality tests (Table 4.7).Homoscedascity is checked by examining the time evolution of the spread ofthe residuals.

4.5 Results

The final estimation results are reported in Tables 4.8-4.14. The coefficientsof the DRAG models are presented in elasticities, while the UCM coefficientsare a priori the regressor estimates. However, since to carry out the UCManalysis, the original data was transformed into natural logarithms, the re-gressor estimates of UCM can be interpreted as the elasticities as well:

ηk =d log Ytd logXkt

=dYtdXkt

· Xk

Y= βk ·

Xkt

Yt(4.1)

To explain the effect of the variables on the response in percentages,

77 4.5. Results

4.2.a)


4.2.b)

79 4.5. Results

4.2.c)


4.2.d)

Fig. 4.2. Residual analysis of road safety measures.


81 4.5. Results

Table 4.8: Exposure.

Variables ACCMOR MORHER MUER HERGRA

(cond. t-stat.) DRAG UCM DRAG UCM DRAG UCM DRAG UCM

VKM 0.382

(1.20)

LAM 1

CONOIL 0.772 0.145

(1.26) (0.16)

LAM 1 LAM 1

COMTOT 0.97 1.195 1.72 0.73 1.137 1.86

(-4.3) (4.44) (-5.29) (-3.1) (3.65) (-6.36)

LAM 1 LAM 1

PRGFUR 2.290 3.813

(1.50) (2.19)

LAM 1 LAM 1

the elasticity estimates for the transformed variables are multiplied by 10,while for the untransformed variable the multiplier coefficient is 100. Sinceeach measure has been estimated using two models, a label of DRAG andUCM will be added to explain the results of a given model. The results andtheir conformity with the traffic accidents literature are discussed in detail asfollows.

4.5.1 Exposure

The elasticities of exposure variables have a positive sign implying that anincrease in exposure increases the frequency and severity of traffic accidents.The results show that a 10% increase in VKM will increase ACCMOR-DRAGby 3.8%. A 10% increase in COMTOT will raise ACCMOR-UCM by 9.7% and, MORHER-DRAG by 11.9%, MORHER-UCM by 17.2%, MUER-UCM by 7.3%, HERGRA-DRAG by 11.3% and HERGRA-UCM by 18.6%.CONOIL and PRGFUR are found to have an effect on fatality-related mod-els (ACCMOR-DRAG and MUER-DRAG) only. In the case of ACCMOR-DRAG the increments are 7.7% and 22.9%, and 1.4% and 38.1% respectivelyfor MUER-DRAG.

4.5.2 Economic factors

Three of the economic factors representing the economic situation, INDCOM,IPI and INDVEN conform to the findings in literature, i.e. a 10% increase


Table 4.9: Economic factors.



INDCOM 0.612

(1.17)

LAM 1

IPI 0.315

(0.73)

LAM 1

INDVEN 0.129 0.127

(1.83) (1.18)

LAM 1 LAM 1

CONST -0.866 -1.638

(-2.79) (-3.91)

LAM 1 LAM 1

PRCOM -0.044 -0.095 -0.289

(-0.11) (-0.54) (-0.61)

LAM 1 LAM 1 LAM 1

INDACT 2.114 1.63 1.856

(0.75) (-2.49) (0.65)

LAM 1 LAM 1

PARO -0.510 -0.21 -0.338 -0.18

(-1.99) (-3.2) (-0.87) (-2.4)

LAM 1 LAM 1

PARSER -0.24 -0.4

(-2.43) (-3.79)

in INDCOM will increase ACCMOR-DRAG by 6.1%, while a 10% increasein IPI will increase MUER-DRAG by 3.1%. A 10% increase in INDVEN willincrease both MORHER-DRAG and HERGRA-DRAG by 1.2%. On the otherhand, investment projects in road safety, such as construction (representedby CONST) and maintenance are found to have a positive effect on roadsafety. The results show that a 10% increase in CONST has a decreasingeffect on ACCMOR-DRAG and MUER-DRAG, estimated as an 8.6% and16.3% reduction respectively.

The results agree with previous work (Chi et al. , 2010, Gaudry and Las-sarre , 2000, Grabowski and Morrisey , 2004) showing that an increase in fuelprices would decrease traffic accident frequency and severity. The estimationresults show that a 10% increase in PRCOM would reduce ACCMOR-DRAGby 0.4%; MORHER-DRAG by 0.9% and MUER-DRAG by 2.8%.

As to the economic activity, the results show that the increase in IN-DACT has a negative impact on road safety (21.1%, 16.3% and 18.5% in-crease in ACCMOR-DRAG, MORHER-UCM and HERGRA-DRAG respec-

83 4.5. Results

tively), while the changes in PARO (5.1%, 2.1%, 3.3% and 1.8% decrease inMORHER-DRAG, MORHER-UCM, HERGRA-DRAG and HERGRA-UCMrespectively) and PARSER (2.4% and 4% decrease in ACCMOR-UCM andMUER-UCM respectively) have a decreasing effect on safety measures.

4.5.3 Driver behavior surveillance

Among the driver behavior surveillance variables CONALC was present inalmost all models and has a positive impact on traffic safety, namely a 10%increase in alcohol controls leads to a 1.7% decrease in ACCMOR-DRAG,0.5% decrease in MORHER-DRAG, 0.6% decrease in MUER-DRAG, 4.5%decrease in decrease in HERGRA-DRAG and 2.8% decrease in HERGRA-UCM. In UC models CONALC was introduced with lagged effect. The resultsshow that a 10% increase in this variable can decrease ACCMOR-UCM by3.8% and MUER-UCM by 1.1%. It is logical to assume that different surveil-lance and control measures lead to effects that are more intense as driversbecome more aware of them. The process of awareness is a lengthy processover time, which explains why the effects are produced with a certain lag.When it comes to breath tests (CONALC), campaigns are run over certainperiods of time. These campaigns are announced through the communica-tions media and implemented by stepping up checks in the period after theannouncement. These checks have a major influence on how drivers perceivethe measure. If we take the year 2001 as reference, 1 out of 10 drivers mayhave been required to take the test. In the most recent period (2008-2010)over 5 million tests were carried out each year, which means 1 out of 4 driverscould have been affected, influencing the propagation process pointed out.

RADAR has a more significant impact on fatality-related measures (AC-CMOR and MUER). The effect is estimated as a 1.9%, 0.2%, 5.3% and0.8% decrease in ACCMOR-DRAG, MORHER-DRAG, MUER-DRAG andHERGRA-DRAG when there is a 10% increment in RADAR.

Both of the suspension-related variables, SUSP and PRLSUSP, are foundto have a positive impact on safety. The estimated elasticities are 3.1%(ACCMOR-UCM), 1.1% (MORHER-DRAG), 3.0% (HERGRA-DRAG) and4.3% (HERGRA-UCM) decrease as the result of SUSP and 2.6% (ACCMOR-DRAG), 1.6% (MORHER-UCM) and 4.5% (MUER-DRAG) decrease as theresult of PRLSUSP.


Table 4.10: Driver behavior surveillance.



CONALC -0.172 -0.38 a -0.051 -0.067 -0.45a -0.118 -0.28

(-1.09) (-6.83) (-0.72) (-0.36) (-7.54) (-1.04) (-6.40)

LAM 1 LAM 1 LAM 1 LAM 1

RADAR -0.190 -0.025 -0.530 -0.087

(-1.16) (-0.38) (-2.44) (-0.98)


PRADAR -0.963

(-2.42)

LAM 1

SUSP -0.31 -0.117 -0.302 -0.43

(-2.63) (-1.06) (-1.86) (-4.82)

LAM 1 LAM 1

PRLSUSP -0.262 -0.16 -0.454

(-1.11) (-1.98) (-2.11)

LAM 1 LAM 1

aThe estimate belongs to the lagged value of CONALC variable.

Table 4.11: Fleet characteristics.



AIRBAG -0.721 -0.15 -0.406

(-1.92) (-3.96) (-1.19)

LAM 1 LAM 1

4.5.4 Fleet characteristics

Among the safety devices included in the models the AIRBAG seemed tohave a significant positive impact on ACCMOR-DRAG, MORHER-UCM andMUER-DRAG; the elasticities being a 7.2%, 1.5% and 4.06% decrease respec-tively.

4.5.5 Road infrastructure

The results show that LONRAC has a decreasing effect on the HERGRA-DRAG model: a 3.7% decrease when there is a 10% increase in LONRAC.

LONRED has a significant effect on the dependent variables. The esti-mations show that a 10% increase in LONRED will have a positive impact

85 4.5. Results

Table 4.12: Road infrastructure.



LONRAC -0.375

(-0.83)

LAM 1

LONRED -1.485 -1.064 -1.61 -2.192

(-1.62) (-3.27) (-7.48) (-2.25)

LAM 1 LAM 1 LAM 2

Table 4.13: Legislative measures.



PPS -0.100 -0.294

(-0.91) (-2.30)

RPC -0.152 -0.333 -0.111 -0.05

(-2.47) (-4.41) (-1.02) (-1.44)

RUIDO -0.008 -0.05

(-0.33) (-3.36)

LAM 1

on road safety, with the estimated effects of a 14.8%, 10.6%, 16.1% and21.9% decrease in ACCMOR-DRAG, MORHER-DRAG, MORHER-UCMand MUER-DRAG respectively. Such a high elasticity can be explained bythe fact that there is usually less traffic on toll roads. Also the geometric char-acteristics (high quality, less curvature, etc.) of these types of roads enhancethe convenience of road users, thus contributing positively to road safety.

4.5.6 Legislative measures

The results show that there was a 10% decrease in ACCMOR-DRAG and a29% decrease in MUER-DRAG since the introduction of the PPS. Accord-ing to the DRAG estimations, RPC introduction has led to a 15.2% reduc-tion in ACCMOR-DRAG, 33.3% decrease in MUER-DRAG, 11.1% drop inHERGRA-DRAG and 5% drop in HERGRA-UCM. RUIDO seemed to have apositive effect on the dependent variable HERGRA, 0.08% and 0.5% decreaseaccording to DRAG and UCM respectively.


Table 4.14: Calendar effect and weather conditions.



DLAB 0.670 2.03 1.911 2.62 0.380

(1.09) (-4.3) (1.88) (-5.03) (1.20)

LAM 1 LAM 1 LAM 1

SDF 0.07 0.017 0.01 0.489 0.11

(-3.47) (0.18) (-1.83) (1.29) (-5.21)

LAM 1 LAM 1

DNIE 0.151 0.006 0.175

(2.47) (0.56) (3.39)

SLNV -0.162 -0.225

(-1.75) (-3.02)

TEMP -0.002

(-0.02)

LAM 1

4.5.7 Calendar effect and weather conditions

As the results suggest, DLAB and SDF generally have a negative impacton road safety. The estimates show that DLAB increases ACCMOR-DRAG6.7%, ACCMOR-UCM 20.3%, MUER-DRAG 19.1%, MUER-UCM 26.2%and HERGRA-DRAG 3.8%, while for SDF the estimates are a 0.7% in-crease in ACCMOR-UCM, 0.1% increase in MORHER-DRAG, 0.1% increasein MORHER-UCM, 4.8% increase in MUER-DRAG and 1.1% increase inMUER-DRAG .

Among the weather condition variables DNIE was found to have a neg-ative effect on safety: 15.1% increase in ACCMOR-DRAG; 0.6% increase inMORHER-DRAG and 17.5% increase in MUER-DRAG, while SLNV had apositive impact (16.2% decrease in ACCMOR-DRAG and 22.5% decrease inMUER-DRAG) on road safety. The positive significant impact of SLNV onfatality-related measures can be explained by the fact that during high snow-depth days, vans do not travel much thus decreasing exposure (Eisenberg ,2004). TEMP was found to have a quite insignificant effect: 0.02% decreasein MUER-DRAG.

4.6 Prediction analysis

The final DRAG and UC models were compared using the prediction resultsby means of a cross-validation exercise: first the models were estimated with

87 4.6. Prediction analysis

the first 108 observations (years 2000-2008) and then the remaining 12 obser-vations (year 2009) were used for prediction (Table 4.15). By analyzing theprediction values and graphs (Figure 4.4) it can be observed that, in the caseof ACCMOR, the volatility of the observed data during the months January-July is relatively better captured by DRAG than by UCM. After this periodthe predictions with both models have an almost linear trend, which do notcapture the seasonality present in the data. In the case of the MORHER,we can see that both models perform equally well. The seasonality of theMUER data however was better captured by the UCM, especially the peaks(January, March, May, October and December) and troughs (April, June,September and November) of prediction with UCM coincide with the truedata. In the case of HERGRA, DRAG seems to have a better prediction per-formance. The graphical analysis in general shows that the seasonality wascaptured relatively better with UCM. This can be due to the fact that theUCM has a specific seasonality component. Prediction accuracy was mea-sured by percentage error, calculated as follows:

PEYt =T∑t=1

100 ·

∣∣∣∣∣(Yt − Yt)Yt

∣∣∣∣∣where yt and yt are the observed and forecast values respectively. The pre-diction errors are reported in Table 4.16. As can be seen, the aggregatedprediction errors produced by DRAG models are lower for all four dependentvariables. In both DRAG and UCM, for the number of accidents with in-jured victims, MORHER (7.6% DRAG y 8.9% UCM) and number of injuredvictims, HERGRA (8.6% DRAG y 13.2% UCM) had a smaller average pre-diction error compared to fatal accidents, ACCMOR (15.5% DRAG y 18.8%UCM) and number of fatalities, MUER (18.9% DRAG y 20.6% UCM).

We can observe that prediction errors are much higher for fatality-relatedmeasures, ACCMOR and MUER, for both DRAG and UCM. Averaging overthe prediction errors of road safety indicators during the summer months(July and August - when traffic safety is especially vulnerable due to high mo-bility and exposure), we can observe that all the DRAG models have a lowerPE (16.3%-ACCMOR; 4.5%- MORHER; 28.6%- MUER; 2%-HERGRA) ver-sus (18.5%-ACCMOR; 5%- MORHER; 31%- MUER; 14%-HERGRA) forUCM (Figure 4.4).


4.3.a.

4.3.b.


4.3.c.

4.3.d.

Fig. 4.3. Observed versus predicted values of four road safety indicators, corresponding

to year 2009.

4.3.a) ACCMOR; 4.3.b) MORHER; 4.3.c) MUER,; 4.3.d) HERGRA.


Table 4.15: A year ahead prediction, year 2009.

Date ACCMOR MORHER MUER HERGRA

DRAG OBS UCM DRAG OBS UCM DRAG OBS UCM DRAG OBS UCM

Jan 16 15 17 104 97 100 19 18 20 118 99 133

Feb 14 15 16 94 91 96 17 15 18 105 100 120

Mar 18 26 21 97 119 99 22 28 24 111 123 123

Apr 16 12 19 98 102 94 18 13 21 106 115 105

May 15 22 20 98 115 97 16 25 24 99 129 119

Jun 19 18 20 112 115 108 20 19 22 132 139 164

Jul 22 21 24 118 122 118 24 21 26 140 136 171

Aug 18 25 20 100 106 99 20 35 22 114 116 114

Sep 18 17 19 99 84 91 21 22 20 110 97 111

Oct 17 23 21 103 106 104 19 26 24 113 108 133

Nov 15 15 18 91 94 90 19 16 20 101 99 101

Dec 17 16 20 101 110 90 18 18 22 113 124 126

Table 4.16: Prediction error in percentage for DRAG and UCM.

Date ACCMOR MORHER MUER HERGRA

DRAG UCM DRAG UCM DRAG UCM DRAG UCM

Jan 6.67 13.33 7.22 3.09 5.56 11.11 19.19 34.34

Feb 6.67 6.67 3.30 5.49 13.33 20.00 5.00 20.00

Mar 30.77 19.23 18.49 16.81 21.43 14.29 9.76 0.00

Apr 33.33 58.33 3.92 7.84 38.46 61.54 7.83 8.70

May 31.82 9.09 14.78 15.65 36.00 4.00 23.26 7.75

Jun 5.56 11.11 2.61 6.09 5.26 15.79 5.04 17.99

Jul 4.76 14.29 3.28 3.28 14.29 23.81 2.94 25.74

Aug 28.00 20.00 5.66 6.60 42.86 37.14 1.72 1.72

Sep 5.88 11.76 17.86 8.33 4.55 9.09 13.40 14.43

Oct 26.09 8.70 2.83 1.89 26.92 7.69 4.63 23.15

Nov 0.00 20.00 3.19 4.26 18.75 25.00 2.02 2.02

Dec 6.25 25.00 8.18 18.18 0.00 22.22 8.87 1.61

91 4.7. Summary and discussions

Fig. 4.4. Prediction errors corresponding to quarterly data.

4.7 Summary and discussions

This research work was triggered by the behavior of severe accidents involv-ing vans that was observed in the Spanish data. The frequency (ACCMORand MORHER) and severity (MUER and HERGRA) of van-involved acci-dents were studied through two established statistical methodologies: UCMand DRAG. The results suggest that the fatality measures, ACCMOR andMUER, are influenced by the same factors, within each type of model (DRAGor UCM). As can be observed, the number of independent variables includedin the DRAG models for the fatality-related measures is higher (17 in AC-CMOR and 19 in MUER respectively) than in the UCM (6 in ACCMORand 5 in MUER respectively). According to DRAG estimation, all of theexplanatory variables categories are present in both ACCMOR and MUER,and the most significant factors belong to the following categories: exposure,driver behavior surveillance, economic factors and legislative measures. UCMestimation, however, includes relatively few significant factors. The factorsthat are common to ACCMOR and MUER belong to the following cate-gories: exposure (COMTOT), economic activity (PARSER), driver surveil-lance (CONALC) and calendar effect (DLAB and SDF). It can be observedthat, when the same factor appears both in DRAG and UCM, the elasticityestimates are nearly the same. This pattern is not observed for DLAB only.

Injury- related measures, MORHER and HERGRA, are affected by the


same factors, within each methodology (DRAG and UCM). Moreover, byanalyzing the results, it can be concluded that the factors are almost common:9 and 8 for DRAG and 8 and 6 for UCM. The most significant variables belongto the following categories: driver behavior surveillance, economic factorsand road infrastructure. The variables with significant estimates generallyhave similar elasticities for both methodologies. For example, in the caseof MORHER the total fuel consumption variable (COMTOT) is included inboth DRAG and UCM and elasticities are 12% and 17% respectively.

Reviewing the results of model estimation, one can say that they makesense and in general conform to the literature. The signs and orders of mag-nitude of the regression coefficients coincide with the literature for all ex-planatory variables in both DRAG and UCM, which is an encouraging indi-cation regarding the adequacy of the models. Besides the model estimationand explanation of the van-involved accidents, the following observations andconclusions can be reached as the result of model comparison:

1. Although not significantly different, in general the DRAG methodologyprovides better predictions than UCM.

2. UCM captures the seasonality during the prediction procedure moreefficiently than DRAG.

3. The UCM prediction accuracy highly depends on the model selectioncriteria- AIC, as mentioned before. In order to get a good fit statisticsvalue the model requirement is to keep statistically significant variablesin the model (in our case this threshold was set as the p-value below10%). Given this threshold and the multicollinearity among the ex-planatory factors the UCM does not allow for the inclusion of so manyregressors as DRAG. The advantage of this is that, since stepwise elim-ination is employed during UCM selection, we obtain a rather small setof candidate models, from which it is quite straightforward to choosethe best model. But since it was of our interest to estimate the ef-fect of many more macroeconomic variables than the UCM thresholdallows us to, it is not really appropriate to apply this class of modelto a macro level with a high threshold. As an example, if we considerthe MORHER model, where the average UCM prediction error is muchless than for the rest of the (UCM) outputs, we can observe that therewere only 7 predictors versus 10 for DRAG. For a traffic accident an-alyst it is straightforward to assume that a model such as MORHERis affected by the macroeconomic variables. However, we can observe


that the UCM applied to this variable only finds significant the effect ofeconomic activity among the economic factor group. But, as mentionedabove, if we try to overcome this problem by including less significantvariables (lower p-values in this case) prediction accuracy will decreaseconsiderably.

4. In DRAG model selection, we have a very large number of candidatemodels. Since there are multiple parameters (BCT parameter, AR errorstructure and regression coefficients for explanatory variables, where theinclusion of the latter can be manipulated by the user), we can end upwith a very large set of models which need to be built, estimated andpredicted separately. This can be considered an advantage since one canalways build a model that outperforms the UCM, as far as estimationand prediction are concerned. But as indicated, having such a large setof DRAG candidate models is a source of difficulty for the user.

Chapter 5

Analysis of fatal accidents:

model selection methodology

5.1 Introduction

When modeling the accident data as a function of a several explanatory vari-ables one issue the researcher is faced with is the choice of parsimonious versusfully specified models (Mannering and Bhat , 2014). The main purpose of thischapter is proposing a macro model selection methodology using somewhatparsimonious SE model structure, where the estimation is based on Bayesianinference (Markov Chain Monte Carlo). The main reason for using Bayesianestimation is the fact that, during Bayesian estimation the model parametersare treated as random variables, which provides a more uniform and thusmore elegant framework to treat uncertainty versus the frequentist approachwhere the parameters are treated as fixed and unknown constants. By usingthe Bayesian approach a model is treated and estimated as a whole (Raftery, 1995) and its adequacy is tested based on criteria such as posterior modelprobability and deviance information criteria (DIC) rather than estimatingeach explanatory variable individually as done during model building usingfrequentist approach. In the past few years Bayesian methods have beenwidely applied to road safety (Mannering and Bhat , 2014).

The proposed model selection methodology addresses the question of pa-rameter (explanatory variables and power transformation) selection and errorautocorrelation. The variable selection was carried out through a method-ology called two-input models (TIM), where several models are constructedusing two inputs and power transformation structure. Given the selected

95

Chapter 5. Analysis of fatal accidents: model selection methodology 96

variables and SE model structure, the final model is selected based on thegoodness of fit measures, such as DIC and pseudo-R2. The selected model iscross validated through prediction analysis. The estimation results are thencompared with the fully specified DR model. The proposed methodology isapplied to the number of monthly fatal accidents in Spain during 2000-2011.

The rest of this chapter is organized as follows. In Sections 5.2 and5.3 the data are discussed. In Section 5.4 the model selection procedure isintroduced. In Sections 5.5 and 5.6 the estimation and prediction results arepresented. The chapter ends with the summary and discussions.

5.2 Fatal accidents

The total number of fatal accidents, ACCTOT , during years 2000-2011 isstudied to address the impact of explanatory factors (Section 2.1.1). Forthe preliminary analysis of the data, the time series was transformed intonatural logarithms. The decomposition of the series into trend and seasonalcomponents was carried out through TRAMO/SEATS (Figure 5.1). As itcan be seen the series has a decreasing trend and seasonal pattern. On a firstvisualization of the series, the observations during July 2000, August 2000,August 2003 and February-April 2010 look like outliers. The estimation ofthe data using the airline model, ARIMA(0, 1, 1)(0, 1, 1)s, however does notdetect any outliers. The modified score test (MAD) for the observation July2000, which has the most extreme value, was 1.64 (< 3.5) thus showing thatthe observation is not an outlier (Table 5.2). The fit statistics of the estimatedmodel are shown in Table 5.1.

5.3 Independent variables

The explanatory variables used as traffic safety factors were divided intothe following groups: exposure, economic factors, driver characteristics andsurveillance, fleet characteristics, road infrastructure, legislative measures,weather conditions and calendar effect (Table 5.3).

5.4 Model selection procedure

As specified in the introduction, the model selection procedure has been ap-plied to the SE models and is carried out within the Bayesian framework

97 5.4. Model selection procedure

Table 5.1: Summary of TRAMO/SEATS results, ACCTOT .

Fit statistics ACCTOT

Mean 265.007

MA1 -0.6425

MA12 -0.9492

BIC -5.1209

SE(at) <0.0001

N(at) 0.4259

Q24(at) 20.78

QS(at) 0.20

Table 5.2: Outlier detection.

Date Value Studentized Values a Studentized Values Median Absolute

Without Deletion With Deletion Deviation (MAD) b

Feb-2010 120.0 -1.85199 -1.88126 -1.50771

Feb-2011 120.0 -1.85199 -1.88126 -1.50771

Apr-2010 123.0 -1.81367 -1.84141 -1.47795

Apr-2011 123.0 -1.81367 -1.84141 -1.47795

Mar-2011 136.0 -1.64764 -1.66938 -1.349

...

Aug-2000 406.0 1.80072 1.82795 1.32916

Aug-2001 422.0 2.00507 2.04112 1.48787

Aug-2002 428.0 2.0817 2.12153 1.54738

Aug-2003 437.0 2.19664 2.24269 1.63665

Jul-2000 438.0 2.20942 2.25619 1.64657

aThe Studentized values measure how many standard deviations each value is from the

sample mean ofbMAD > 3.5 might be an outlier


Fig. 5.1. Decomposition of ACCTOT into trend-cycle and seasonal components with

TRAMO/SEATS.


Table 5.3: Explanatory variables, 2000-2011.

Variable Definition

Exposure

VHP Heavy Vehicles

VKM Vehicle Kilometers Travelled

CONGAS Gasolne Consumtion

Economic factors

IPI IPI

PRDCRN Meat Production

CONCEM Cement Consumption

MANT Maintenance Investment

PREC Fuel Price

OCUP1 Total Employed

OCUP2 Employment Construction Sector

PARO Total Unemployment

Driver characteristics and surveillance

COND2 Young Drivers (2 years)

CONALC Random Alcohol Checks

RADAR Speed Controls

SUSP Driving License Suspended


VEH10 Vehicle Age (10 years), % of Total Fleet

ABS ABS Equipped, % of Total Fleet

Road infrastructure

LONRAC High Capacity Roads, % of Total Network

LONRED Length of Toll Roads


PPS Penalty Point System

RPC Penal Code Reform

Weather conditions

PREC Rainfall

DNIEB Foggy Days

SLNV Number of Days with Snow Covered Ground

HSOL Amount of Sunny Hours

Calendar effect

DLAB Working days

SDF Weekend and Holidays

SEMSAN Easter Break


through MCMC estimation. The procedure is based on the application oftwo-input models (TIM) and consists of three stages implemented sequen-tially: 1. explanatory variable selection; 2. power transformation estimation;and 3. final model selection:

1. Stage 1: Selection of explanatory variable.

1.1 Build a set of two-input models (TIM), using 28 explanatory variables,thus each model contains a combination of two variables. There are(282

)= 378 combinations and thus 378 possible models. The model

structure is as given by equations (3.9)-(3.10), i.e. SE withAR(2) errors.The model parameters are assigned non-informative prior distributions.TIMs facilitate the selection of variables across the models and help topartially take care of the multicollinearity among independent variablesas it will be detailed in 1.4.

1.2 The explanatory variables belonging to the same TIMs are transformedwith the same value of Box-Cox transformation value, λX , while the de-pendent variable is not. There are three fixed values of λX = (−0.5, 0.1,0.5). Variables belonging to each TIM are transformed with the samevalue of λX . Given that there are 378 variable combinations and threeBCT values λX , a total of 3 · 378 = 1134 models are estimated.

1.3 Sort the TIMs by goodness of fit measure, pseudo-R2. Higher pseudo-R2 value means better fit. For each value of λX , select the first 50 TIMswith the best goodness of fit measure thus, a total of 3 · 50 = 150 TIMsare selected.

1.4 The first stage is completed by selecting the explanatory variables. Todo this, among the selected 150 TIMs, the ones that were repeated 3times (i.e. for the three values of λX) were selected. Selection based onthis method avoids the problem of selecting one variable based on itspower transformation, i.e. if a given variable achieves a better estima-tion with a given value of BCT then there is a probability that severalTIM’s that contain this variable will have a better goodness of fit mea-sure and can fall within the 50 models threshold. The same variable canalso appear in the models with higher goodness of fit measures becauseof being highly correlated with the other explanatory variables. Then ifthe variables are selected solely based on the fact that they appear threeor more times across three sets of 50 selected models, it can’t be assuredwhether the same variable appear in all three sets of selected 50 models


or the same variable appears more than once in one set of model andnone in the other. Thus selecting the TIMs rather than variables canensure that a given variable achieves a better fit with all three valuesof λX and the problem of multicollinearity can be somewhat avoided.

2.1 Stage 2.1: Estimation of power transformation parameter for the re-sponse.

2.1.1 Using the explanatory variables selected in Stage 1 optimize the BCTvalue for the dependent variable with respect to λY . For this purposean algorithm by Venables and Ripley (Venables and Ripley , 2002)was used. The explanatory variables were kept untransformed. Theoptimization is carried out through log-likelihood estimation.

2.2 Stage 2.2: Estimation of power transformation parameter for the ex-planatory variables.

2.2.1 Build a model using the explanatory variables selected in the first stage.The model has the same form as in equations (3.9)-(3.10) (Chapter 3).Both the dependent and independent variables are power transformed.The dependent variable is transformed using the optimal λY obtained inStage 2.1. The explanatory variables are divided into groups describedin Table 5.3 and power transformed using three previously fixed valuesof λX = (−0.5, 0.1, 0.5). Considering that one group of variables canperform better by transforming under one λ than other, all the possi-bilities are considered by transforming the variables belonging to thesame group with the same value of λX . For computational purposes thedummy and quasi-dummy variables are not transformed. A total of 3N

models are constructed, where N is the number of groups.

3. Stage 3: Final model selection according to goodness of fit measure andthe expected signs of explanatory variables.

3.1 Determining the expected signs of the explanatory variables selected inStage 1 based on the literature review. The model adequacy requiresthat the direction of the effect (i.e. the signs of the explanatory vari-ables) agrees with the results from the previous empirical studies.

3.2 Model selection based on goodness of fit measures (DIC) and interpre-tation of the model variables. A lower DIC value means a better fit.

4. Stage 4: Cross-validation through prediction.


Table 5.4: Stage 1: Pseudo-R2 values of selected two-input models for

three different values of power transformation, λX .

Pseudo R2

TIM X1 X2 λX = −0.5 λX = 0.1 λX = 0.5

28 V KM CONGAS 0.804 0.803 0.815

107 OCUP1 MANT 0.867 0.837 0.802

236 PRECOM LONRAC 0.834 0.833 0.810

314 CONALC SUSP 0.823 0.812 0.811

325 RADAR V EH10 0.819 0.819 0.835

327 RADAR LONRAC 0.810 0.828 0.836

329 RADAR PPS 0.820 0.810 0.811

334 SUSP V EH10 0.804 0.810 0.810

346 V EH10 PPS 0.803 0.804 0.802

4.1 The final model is cross validated through prediction. For this purposethe last 12 observations are estimated.

5.5 Results

In this Section the results of the model selection strategy and comparisonwith the DR model are presented.

5.5.1 Explanatory variable selection

The explanatory variable selection was carried out through the above pro-posed TIM methodology (Stage 1). The estimation methodology is MCMCwhich was implemented using R and WinBUGS (Lunn et al. , 2000) soft-wares (see Appendix III for WinBUGS code). The Gibbs sampler was runin 20, 000 iterations in 3 chains. The model convergence was checked usingtrace plots. In this stage a total of 378 · 3 = 1134 models were estimated (seeAppendix IV for WinBUGS outcome for variable selection stage). Among theselected 150 TIM’s 9 TIMs consisting of 11 variables were selected: V KM ,CONGAS, OCUP1, MANT , PRECOM , CONALC, RADAR, SUSP ,V EH10, LONRAC and PPS (Table 5.4). The selected explanatory vari-ables belong to 6 categories, namely exposure, economic factors, driver be-

103 5.5. Results

Table 5.5: Explanatory variables selection.

Group Variables SE model

Exposure VHP

VKM 3

CONGAS 3

Economic IPI

factors CONCEM

PRDCRN

MANT 3

PRECOM 3

PARO1

OCUP1 3

OCUP2

Driver COND2

characteristics CONALC 3

and surveillance RADAR 3

SUSP 3

Vehicle VEH10 3

characteristics ABS

Road LONRED

infrastructure LONRAC 3

Legislative measures PPS 3

RPC

Weather PREC

conditions HSOL

SLNV

DNIEB

Calendar SDF

effect SEMSAN

DLAB

havior surveillance, vehicle characteristics, road infrastructure and legislativemeasures.

5.5.2 Estimation of power transformation parameter

The transformation value for the dependent variable (SE model) was op-timized using the selected 11 explanatory variables. The optimal λY wasselected from the same interval as the λX , λ ∈ [−0.5, 0.5]. The optimal valuefor λY was set to λY = 0.25 (Figure 5.2).

The explanatory variables selected as the outcome of the input variablesselection procedure (stage 1) are grouped into 6 categories (Table 5.6). The


Fig. 5.2. BCT optimization, Yt.

explanatory variables belonging to the same category were transformed withthe same value of λX . Since one of the groups consists of a single dummyvariable (PPS), this variable group is not subject to the power transformation.Thus, considering that there are 5 input variable groups subject to powertransformation and 3 fixed values of λX = (−0.5, 0.1, 0.5), a set of 35 = 243models were constructed, where the explanatory variables are transformedwith 3 different values of λX .

5.5.3 Model selection

For final SE model selection the models were constructed using the selected11 variables and the power transformation values. The MCMC estimationwas applied to a total of 243 models using three chains taken to 100, 000 it-erations (see Appendix V for WinBUGS outcome for model selection stage).Final model selection was based on the correct signs of the selected vari-ables according to previous empirical research on road safety (Table 5.6) andgoodness of fit measures (DIC values).

The estimation results indicate that 10 out of 243 the models fit thedata as far as the variable signs are concerned. As it can be observed inTable 5.7 pseudo-R2 value is around 0.94 across the models, thus the selected

105 5.5. Results

Table 5.6: Selected variables and the expected signs, based on previous

empirical studies.

Group Description Variable Expected

sign

1. Exposure V KM +

CONGAS +

2. Economic OCUP1 +

factors MANT -

PRECOM -

3. Driver surveillance CONALC -

RADAR -

SUSP -

4. Vehicle characteristics V EH10 +

5. Road infrastructure LONRAC -

6. Legislative measures PPS -

Table 5.7: Fit statistics of selected 10 SE models.

Models Fit statistics

Pseudo- R2 DIC

SE122 0.9398 88

SE128 0.9354 92

SE155 0.9377 92

SE161 0.9379 92

SE203 0.9391 90

SE204 0.9394 88

SE207 0.9401 86

SE212 0.9401 89

SE213 0.9401 88

SE215 0.9388 88


11 variables explain around 94% of model variability in general.

The model SE207 has the lowest DIC (= 86) value, and highest pseudo-R2 (= 0.94). The estimation results of elasticities for SE207 (Table 5.9) showthat a 10% increase in V KM , CONGAS, V EH10 and OCUP1 will increasethe number of fatal accident by 1.3%, 2.6%, 3.6% and 27.9% respectively.While a 10% increase in MANT , PRECOM , CONALC, RADAR, SUSPand LONRAC will reduce the accident rate by 6.2%, 1.4%, 0.1%, 0.6%, 6.9%and 9.9% respectively. The effect of PPS is counted as a 1.1% decrease infatal accident frequency.

The results of the variable selection (TIM, 5.5.1) indicates that amongthe initial 28 variables, the selected variables with a positive impact on roadsafety are two economic variables, MANT and PRECOM , four surveillanceand legislative factors, CONALC, RADAR, SUSP and PPS, and a roadinfrastructure variable, LONRAC. The results of model selection procedureindicates that economic and infrastructure variables have relatively higherimpact compared to surveillance and legislative factors (Table 5.9). This canbe observed in the elasticities. However the standard deviation associated tothese estimates are higher compared to those of surveillance and legislativemeasures, meaning that the elasticity estimates for the latter factor group isrelatively unbiased compared to the previous groups and can be consideredas real effects.

The variables with the negative effect on safety are exposure (V KM andCONGAS), vehicle age (V EH10) and employment (OCUP1), as selected bythe TIM procedure. The selected variables support the previous findings inthe road safety literature. The effects vary between 1-4%, for the exposureand vehicle age, except for OCUP1, which is almost 28%. However thestandard deviation for this estimate is relatively higher. In general, it can beobserved that the elasticity estimates with relatively higher coefficients havea corresponding higher standard deviation. This is true for all the variables,OCUP1, MANT and LONRAC, except for SUSP .

5.5.4 Dynamic regression model

As mentioned above, the selected model was compared with the DR model.The DR model was built using the selected 11 variables. The model selec-tion was based on the Ljung-Box (LBQ) test of residuals and AIC statis-tic. The error structure of the first DR model, DR1, was first obtainedthrough an automatic procedure. The final error structure was selected asARIMA(1, 0, 0)(0, 0, 0)s. The AIC statistic for this model was −278.97,

107 5.5. Results

Table 5.8: Fit statistics of DR models.

Fit Models

statistics DR1 DR2

AIC -278.97 -270.70

BIC -238.61 -224.70

σ2 0.0057 0.0056

LBQ(12) 23.56 25.05

(p−value) 0.0233 0.0145

LBQ(24) 37.88 42.18

(p−value) 0.0357 0.0123

Observations 132 132

Table 5.9: Estimation results of selected models, DR2 and SE207.

Parameters DR2 SE207

Elasticity(%) S.D. Elasticity(%) S.D. BCT

Variables

V KM 2.3 -0.096 1.3 0.016 λX = 0.5

CONGAS 3.2 0.197 2.6 0.058 λX = 0.5

V EH10 3.1 0.424 3.6 0.484 λX = 0.5

OCUP1 11.0 0.263 27.9 3.150 λX = 0.1

MANT -2.9 0.264 -6.2 4.451 λX = 0.1

PRECOM -0.7 0.131 -1.4 4.548 λX = 0.1

CONALC 0.0 0.045 -0.1 0.535 λX = 0.1

RADAR -0.8 0.048 -0.6 0.204 λX = 0.1

SUSP -1.7 0.066 -6.9 0.995 λX = 0.1

LONRAC -14.4 0.518 -9.9 14.250 λX = 0.5

PPS -2.3 0.056 -1.1 0.232 NA

Coefficient Coefficient

estimate S.D. estimate S.D.

Other parameters

φ1 0.1493 0.149 0.1858 0.099

φ2 0.1355 0.136 0.1450 0.105

φ12 0.1334 0.133

θ1 0.0203 0.020

τ 9.9150 1.256


while the LBQ test of first 12 and 24 lags were equal to 23.56 and 33.89 withp−values 0.0233 and 0.0145 respectively (Table 5.8).

The errror structure of second DR model, DR2, was selected as ARIMA(2, 1, 1)(1, 0, 0)s. The fit for this model improved compared to DR1, withAIC = −270.7. The LBQ test of first 12 and 24 lags were equal to 25.05 and42.18 with p−values 0.0357 and 0.0123 respectively (Table 5.8). The selectedDR model thus has the following form:

∇Yt =11∑k=1

βkXkt +1− θ1B

(1− φ1B − φ2B2)(1− φ12B12)swt (5.1)

σ2w = 0.0056 (5.2)

The estimation results for the DR2 model (Table 5.9) indicate that a10% increase in V KM , CONGAS, V EH10 and OCUP1 will increase thenumber of fatal accident by 2.2%, 3.1%, 3.0% and 10.9% respectively, whilea 10% increase in MANT , PRECOM , CONALC, RADAR, SUSP andLONRAC will reduce the accident rate by 2.9%, 0.7%, 0.01%, 0.7%, 1.7%and 14.4% respectively. The effect of PPS is counted as a 2.2% decrease infatal accident frequency. The estimation results of DR2 model are very closeto those of model SE207. As in the case of SE207, the economic factorsseem to have a higher impact on the road safety measure, ACCTOT , com-pared to surveillance factors and policy measures. In general the elasticityestimates of DR2 model follow the same hierarchical order as of the SE207.However, unlike the SE207, higher elasticity values are not associated withthe higher standard deviations. It can be observed that in fact the standarddeviations are smaller, thus the estimates can be considered as less biased.One can observe that as far as the variable estimation is concerned the resultsof DR2 estimation conform to the existing literature, i.e. exposure, vehiclecharacteristics and economic variables indicating the employment rate havea negative impact, while surveillance and legislative measures, road infras-tructure and economic factors related to investment and fuel prices have apositive impact on road safety indicator, ACCTOT . As a result the variableselection methodology can be considered as effective one.

109 5.5. Results

Table

5.1

0:

Pos

teri

orp

red

icti

onin

terv

als

ofse

lect

edm

od

els.

Par

amet

ers

Ob

serv

edD

R2

SE

207

Low

P.I

.(9

5%)

Pre

dic

ted

Hig

hP

.I.

(95%

)L

owP

.I.

(95%

)P

red

icte

dH

igh

P.I

.(9

5%)

Jan

-11

129

129

150

174

118

147

180

Feb

-11

117

125

145

168

111

142

174

Mar

-11

118

129

150

174

116

146

182

Ap

r-11

122

140

163

190

126

161

200

May

-11

149

132

153

178

117

148

183

Ju

n-1

112

713

816

118

812

615

619

5

Ju

l-11

183

156

181

211

141

176

219

Au

g-11

176

152

177

206

140

176

216

Sep

-11

150

136

159

185

120

154

195

Oct

-11

139

129

151

175

115

145

182

Nov

-11

139

119

139

162

104

133

167

Dec

-11

134

131

152

177

108

144

195


Table 5.11: Prediction accuracy of selected models

Measure DR2 SE207

MAE 16.76 14.42

MSE 468.68 361.08

MAPE 13.29 11.43

5.6 Prediction analysis

The prediction analyses were conducted for cross validation and comparisonpurpose of the model estimation results. For estimation, 132 observationswere included in the model while the remaining 12 observations were usedto assess prediction performance. The SE207 model estimation starts afterperiod t = 3. New observation values of dependent variables are predicted byemploying the MCMC estimates of the parameters obtained from the resultsof model selection. The Gibbs sampler was run in 100, 000 iterations in 3chains. To evaluate the prediction performance of the model, 95% posteriorprediction intervals were computed. As can be seen in Figure 5.3 all obser-vations, except for April − 2011 fall within the posterior prediction interval,namely 92% of the observations fall within the prediction interval estimatedby the SE207 model.

The predicted values through the DR2 model are very close to thoseof SE207 model. However only 7 out of 12 observations, i.e. 58% of theobservations, fall within the prediction interval estimated by the DR2 model.

In order to compare the prediction performance of the models the pre-diction accuracy of the models were computed using three measures: meanabsolute error (MAE), mean squared error (MSE) and mean absolute predic-tion error (MAPE), where:

MAE =1

n

n∑t=1

∣∣∣Yt − Yt∣∣∣ (5.3)

MSE =1

n

n∑t=1

(Yt − Yt

)(5.4)

MAPE =1

n

n∑t=1

100 ·

∣∣∣∣∣(Yt − Yt)Yt

∣∣∣∣∣ (5.5)

It can be observed from Table 5.11 that SE207 has the smaller prediction


5.3.a.

5.3.b.

Fig. 5.3. Prediction intervals for selected models.

5.3.a) SE207; 5.3.b) DR2


error that the DR2 model, for all prediction accuracy measures.


The objective of this chapter was the analysis of fatal road accidents in Spainduring 2000-2011 and the determination of the factors that had a majorimpact on it.

Although there are numerous statistical methodologies applied to theanalysis of road safety analysis, the selection of appropriate methodology fora given data and thus the model selection has not been thoroughly studiedand there is still a lack of formal guidance on how the variables are selectedand how to carry out the estimation. This problem specially prominent whenmacroeconomic data such as fatal accidents for a whole region or countryare concerned. The main objective of this chapter was thus to propose amodel selection methodology where the explanatory factors that have a majorimpact on road safety measures were determined.

For this purpose a model selection strategy using SE model and MCMCestimation was proposed. The model used in the study is parsimonious. Theexplanatory variable selection procedure has used models with combinationsof only two explanatory variables. This restriction adopted for simplicity hasproved adequate in view of the results. Given the model variables and set ofpower transformation values the methodology allows to build all the possiblemodels and select the most adequate one among these models. By limitingthe initial number of parameters (AR structure of the error term and thepower transformation values) to few values, the focus on the model selec-tion procedure is on the explanatory variable selection and BCT parameterestimation for both explanatory and response variables.

The variable selection procedure based on TIMs achieves rather efficientresults, in terms of road safety analysis. As it can be observed the selectedvariables are highly relevant factors in the road accidents, e.g. exposure,vehicle age, surveillance and legislative factors, etc. The variable selectionprocedure considers all the possible combinations of inputs, thus eliminatingthe possibility of discarding important inputs, as it is usually done during theother variable selection procedures such as stepwise elimination for example.The results of the model selection procedure are very intuitive and closelyfollow those obtained in previous empirical studies on road safety analysis.Moreover, the prediction analysis yields better results compared to a fullyspecified DR model. The methodology has thus proved to be successful in


providing a quick, simple and effective model selection strategy, which couldeasily be sophisticated and generalized with some additional but feasible com-putational cost.

Chapter 6

Simulation experiment based

model comparison methodology

with application to road

accident models

6.1 Introduction

The purpose of this chapter is the development of a methodology for the-oretical comparison of two statistical models, with an application to macromodeling of time series road accident data. It often occurs in applied statisticsthat two or more alternative models compete to describe the data generatingprocess in hand. It is then of great interest to understand the similarities anddifferences between the two models from a theoretical point of view. Ideallythis would be done analytically, but this is very often an unfeasible solution,it is thus necessary to apply Monte Carlo simulation to replace theorems.The methodology proposed for the theoretical comparison is based on MonteCarlo simulations and leans on computer experiment design and ANOVA.

The methodological choice of statistical models is a topic of high interestin road accident data modelling. Accidents are assumed to be the outcomeof complex random processes whose general characteristics can be estimatedthrough statistical models. Normally the choice of statistical model for thispurpose will depend on the data, since the preference of one model over an-other can not often be proven mathematically. However, even with the same

115

Chapter 6. Simulation experiment based model comparison methodologywith application to road accident models 116

data, comparison of models can leave much to be desired in terms of provid-ing a statistical evidence, Mannering and Bhat (2014). Considering theseissues, the main goal of this chapter is, given two competing statistical mod-els applied to road accident data, to relate them by obtaining the samplingdistributions of parameter estimates of one of the models when the true datagenerating process is the other model.

Monte Carlo simulation has been, since the 50’s (Metropolis et al. ,1953) an essential tool of numerical mathematics, with applications to solvingpartial differential equations (PDE), optimization, or numerical integration.Relevant references for these applications are Sabelfeld (1989) for solvingPDE’s, or Kroese et al. (2011) for a handbook of techniques. Statisticalapplications are mainly concerned with numerical integration in, for exam-ple, Bayesian inference or optimization for maximum likelihood estimation(Robert and Casella , 2004). Generally speaking, Monte Carlo simulationcan be in many situations more successful or even the only feasible alterna-tive versus traditional numerical techniques.

The modelling of time series road accident data is carried out taking intoaccount the autocorrelated errors. Two ways of modelling this phenomenonis either modelling the errors using Box-Jenkins ARIMA models or filteringout the unobserved components such as trend and seasonality. A special caseof the first type of models are the DRAG family models (Demand for Roaduse, Accidents and their Gravity) (Gaudry , 1984, Gaudry and Lassarre ,2000), where the errors are treated as an autoregressive (AR) process. Thesecond class of models that have been used in road safety literature are theunobserved components model (UCM) (Harvey and Durbin , 1986).

The comparison of two types of models can be carried out in termsof interpretation of one model type through the other. This approach hasbeen used by some authors in time series literature (Harvey and Scott , 1994,Hillmer and Tiao , 1982, Maravall , 1985), where UCM has been interpretedas Box-Jenkins ARIMA. Nevertheless, in practice the autocorrelation model-ing of DRAG does not cover all the ARIMA model range since it is restrictedto AR structures. Although it is not very clear how a stationary model likeDRAG would capture UCM trend and seasonality, we could guess that theywould be picked up by the DRAG autoregressive error term. If this is thecase, then using either UCM or DRAG to model road accident data will yieldunbiased regression coefficients. If, on the contrary, the regression coeffi-cients partially pick up the trend and/or seasonality the estimation of effectswould be biased. Thus, there is a need for more precise quantification on thecorrespondence between both kinds of models, which can be done through

117 6.2. Simulation experiment methodology

simulation, since, as mentioned above, analytical tools become cumbersomeor nearly unfeasible. Moreover, in the context of road accident modeling anaccurate estimation of factor effects, particularly of countermeasures carriedout by administrations, is important for the decision makers in a very relevantsocial problem.

This chapter is organized as follows. In Section 6.2 the experimental de-sign study is described followed by the introduction of the previous empiricalstudy in Section 6.3. The results of the simulation experiment methodologyare presented in Section 6.4. Finally, in Section 6.5 the summary and somediscussions are presented.

6.2 Simulation experiment methodology

The methodology consists in generating samples of a UCM and observing howthe distribution of the parameter estimates of the DRAG model are relatedto the parameter values of the simulated UCM. Each UCM parameter willbe ”captured” by a specific subset of the DRAG estimates; for example itis reasonable to expect that a UCM regression coefficient will be capturedby the corresponding DRAG coefficient but there is uncertainty about whichDRAG coefficient will capture the effect of the UCM trend parameter.

In order for the generated data to be as close as possible to the realroad accident data, the simulation was carried out using the parameter esti-mates from previous UCM modeling of van-involved accident data providedby Spanish Accident Data Base (Dadashova et al. , 2014).

The simulation experiment methodology has the following steps (Figure6.1):

1. Designing a simulation experiment covering the range of the parametersof the unobserved components model (UCM). These ranges have beenestimated from the results of previous empirical work, as detailed inSection 6.3.

2. Generate samples of UCM with the parameters of the design of step 1.

3. Estimate DRAG models using the UCM samples generated in the sec-ond stage. The DRAG models were constructed following standardpractice, with a selection based on the goodness of fit measures.

4. Estimate the relationship between UCM and DRAG parameters throughANOVA. ANOVA provides quantification of how the variability of the


Fig. 6.1. Simulation methodology.

DRAG estimates is disaggregated into the contributions of the UCMparameters, either individually (main effects) or jointly (interactions).

In the next section the results of the empirical study mentioned in step1 is reviewed, to establish the parameter ranges in the experiment, and sub-sequently explain in detail the four steps above.

6.3 Empirical study

The empirical study (Dadashova et al. , 2014) used for generating the samplesfor the simulation study is described below. The objective of the researchwork was to estimate the effect the different factors had on the number of thetraffic accidents involving vans (ACCMOR) using the unobserved componentsmodel.

6.3.1 Data

The empirical analysis was carried out using the monthly data on van-involvedtraffic accidents in Spain. The data cover the period from 2000-2009. Theresponse variable is the number of fatal accidents (ACCMOR). The fol-lowing explanatory variables were included in the model: fuel consumption(COMTOT ), number of random surveillance breath tests (CONALC), num-ber of driving license suspended (SUSP ), unemployment in service sector(PARSER) and number of working days (DLAB), (Table 6.1).

119 6.3. Empirical study

6.3.2 Model estimation

The data was converted into the natural logarithms and the final model wasobtained through two stages: descriptive and explanatory analysis. In thefirst stage the accident frequency was analyzed by decomposing the data intothree descriptive - level, slope and seasonal components. There are two stepsto consider while including the descriptive components in the model, first isto decide whether the component is time varying, second whether it is con-tributing to the response variability. The components can enter the modeleither stochastically (non zero variance) or deterministically (zero variance)and are included in the model if significant. The significance level, in this casethe p-value was set to be below 10%. The final descriptive model was selectedaccording to the Akaike Information Criteria (AIC) and the significance ofthe descriptive components (Table 6.2). According to the estimation out-come the final descriptive model was defined as a deterministic linear trend(σ2ζ = σ2

κ = 0)

with no seasonal component.

In the second stage the explanatory variables were introduced to thedescriptive model and the final model was selected based on the AIC and thesignificance of the regressor, with the significance below 10%. For this pur-pose the stepwise elimination procedure was used. Also the multicollinearityamong the regressors was taken into account. Finally the residual analysis ofUCM was carried out by checking the validity of the hypothesis of normality,homoscedasticity and independence of the errors (Figure 6.2). The followingvariables were kept in the model: COMTOT , CONALC, SUSP , PARSERand DLAB (Table 6.2). Thus the final UCM used for the empirical studyhave the following form:

YACCMOR = δPARSER ·X1,t + δCONALC ·X2,t + δSUSP ·X3,t+

+ δDLAB ·X4,t + δCOMTOT ·X5,t + εt (6.1)

where εt is i.i.d. with N(0, σ2ε).

Table 6.1: Explanatory variables.

COMTOT Fuel consumption

CONALC Number of random surveillance breath tests

SUSP Number of driving license suspended

PARSER Unemployment in service sector

DLAB Working days


6.2.a

6.2.b

6.2.c

Fig. 6.2. Residual analysis of ACCMOR

6.2.a) Distribution of residuals; 6.2.b) Residual autocorrelation; 6.2.c) Residual

white noise test.

121 6.4. Experimental design: estimation and results

Table 6.2: Results of empirical study: fit statistics and parameter

estimates.

Fit statistics

Full Log Likelihood 248.06

AIC (smaller is better) -47.61

BIC (smaller is better) -44.88

Regessors Estimatesa

δPARSER -0.24

δCONALC -0.38

δSUSP -0.31

δDLAB 2.03

δCOMTOT 0.97

σ2ε 0.05

aUCM regressor estimates are considered as the elasticities as well.

6.4 Experimental design: estimation and re-

sults

6.4.1 Experimental design

The experimental design study begins with the simulation of data. As indi-cated, for this purpose the parameter estimates from previous work (Dadashovaet al. , 2014) were used, in order to obtain proxy samples that would replicatethe accident data as close as possible. The model in the reference, equation(6.1), however does not include some of the terms, i.e. an intervention variableand an unobserved component (trend/seasonality), with which the originalUCM (Harvey and Durbin , 1986) had been built. Thus in order to obtaindata samples that would satisfy the conditions of UCM, the equation (6.1)was re-formulated including a stochastic trend, with a non-zero variance (σ2ζ 6= 0) and an intervention variable, Reform Penal Code (RPC):

YACCMOR = δPARSER ·X1,t + δCONALC ·X2,t + δSUSP ·X3,t+

+ δDLAB ·X4,t + δCOMTOT ·X5,t + δRPC · ωt + εt (6.2)

µt = µt−1 + ζt (6.3)


Table 6.3: Parameter estimates.

Main effects UCM param. Values

Level I Level II

A δPARSER -0.24 -0.19

B δCONALC -0.38 -0.30

C δSUSP -0.31 -0.24

D δDLAB 2.03 1.62

E δCOMTOT 0.97 0.77

F σ2ζ 0.020 0.025

where εt and ζt are i.i.d. with N(0, σ2ε) and N(0, σ2

ζ ) respectively, and δk areregression coefficients and ωt is dummy variable with coefficient δRPC thattakes values:

ωt =

{0, if t < 961, if t ≥ 96

(6.4)

where 96th observation corresponds to the date (December 2007) when PenalCode Reform was enacted.

The presence of stochastic term is considered to be very important. Asit was seen in chapter 5, the true data when modelled through DR modelincluded an integration term of order 1, ∇ = 1 (equation (5.2)). Howeverin a stationary model like DRAG there is no separate term for a stochasticcomponent. Thus it is crucial to see whether the stochastic trend, if present inthe true data, should be modelled and treated separately (e.g. by differencingof the data beforehand).

Thus there are a total of 6 parameters set as the factors of the computersimulation experiment instead of only 5 variables, as described in Table 6.3:5 regression coefficients, δPARSER, δCONALC , δSUSP , δDLAB, δCOMTOT and atrend variance, σ2

ζ . The values of δRPC and σ2ε were kept as constant. Each

factor takes two values, the first level values are the UCM estimates (Table6.2). The second level values of UCM regressors are obtained by multiplyingthe estimate values by 0.8 (Table 6.3). The multiplicator is set to 0.8 withthe purpose of generating sample paths of response variable that are withina reasonable range and avoid generating the sample paths with close values.The second level value of trend variance, σ2

ζ was selected as the result of theapproximate calibration with respect to the real data. A full factorial designwas built with the 26 combinations of the 2 levels of six parameters. Thereare no replications.

123 6.4. Experimental design: estimation and resultsS

Pa

SV

bP

aram

eter

esti

mat

esF

itst

atis

tics

η PARSER

η CONALC

η SUSP

η DLAB

η COMTOT

λρ1

ρ2

Log

-li.

R2 1c

R2 2d

1O

-0.6

2-0

.34

-0.1

90.

810.

28-0

.32

0.30

0.17

-291

.727

0.93

30.9

28

2A

-0.6

0-0

.34

-0.1

90.

810.

29-0

.32

0.30

0.17

-326

.398

0.93

30.9

27

3B

-0.6

3-0

.31

-0.1

90.

820.

28-0

.34

0.30

0.17

-339

.667

0.92

80.9

22

4C

-0.6

2-0

.34

-0.1

60.

810.

29-0

.32

0.30

0.17

-321

.721

0.93

20.9

26

5D

-0.6

3-0

.34

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90.

630.

28-0

.32

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-228

.495

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20.9

27

6E

-0.6

2-0

.34

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90.

810.

20-0

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0.30

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-214

.177

0.93

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30

7F

-0.1

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10.

780.

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927

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0.82

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300.

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9A

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.60

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0.29

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30.

300.

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63.1

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932

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10A

D-0

.60

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0.28

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30.

300.

17-2

48.8

490.

934

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29

11A

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.60

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4-0

.19

0.81

0.20

-0.3

20.

300.

17-3

69.6

590.

926

0.9

20

12B

C-0

.63

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1-0

.16

0.81

0.28

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40.

300.

17-2

76.4

330.

927

0.9

21

13B

D-0

.63

-0.3

1-0

.19

0.64

0.28

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40.

300.

16-2

62.1

160.

930

0.9

24

14B

E-0

.62

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1-0

.19

0.81

0.20

-0.3

30.

300.

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58.4

850.

930

0.9

25

15C

D-0

.63

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0.63

0.29

-0.3

30.

300.

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44.1

700.

933

0.9

28

16C

E-0

.62

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0.20

-0.3

20.

300.

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50.9

500.

934

0.9

29

17D

E-0

.63

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0.63

0.20

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20.

300.

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310.

925

0.9

19

18A

F-0

.08

-0.2

0-0

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0.78

0.63

0.13

0.16

0.25

-311

.107

0.92

60.9

20

19B

F-0

.10

-0.1

7-0

.11

0.78

0.63

0.16

0.16

0.25

-296

.790

0.92

90.9

23

20C

F-0

.10

-0.2

0-0

.08

0.78

0.63

0.11

0.16

0.25

-293

.157

0.93

00.9

24

21D

F-0

.10

-0.2

0-0

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0.61

0.63

0.15

0.16

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-185

.623

0.93

30.9

28


SPa

SV

bP

aram

eter

esti

mat

esF

itst

atis

tics

η PARSER

η CONALC

η SUSP

η DLAB

η COMTOT

λρ1

ρ2

Log

-li.

R2 1c

R2 2d

22E

F-0

.10

-0.2

0-0

.11

0.78

0.54

0.13

0.16

0.25

-278

.842

0.93

20.9

27

23A

BC

-0.6

0-0

.31

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60.

810.

28-0

.35

0.30

0.17

-306

.421

0.92

50.9

19

24A

BD

-0.6

1-0

.31

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90.

640.

28-0

.35

0.30

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-292

.107

0.92

80.9

22

25A

BE

-0.6

0-0

.31

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90.

810.

20-0

.34

0.30

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-198

.888

0.92

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23

26A

CD

-0.6

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630.

29-0

.34

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0.92

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27A

DE

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90.

630.

20-0

.33

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28A

CE

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810.

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0.92

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21

29B

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630.

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21

30B

CE

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60.

810.

20-0

.34

0.30

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26

31B

DE

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90.

640.

19-0

.34

0.30

0.16

-233

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0.92

80.9

22

32C

DE

-0.6

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60.

630.

28-0

.36

0.30

0.17

-263

.548

0.92

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19

33A

BF

-0.0

8-0

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10.

780.

630.

160.

160.

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300.

772

0.7

53

34A

CF

-0.0

8-0

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-0.0

80.

780.

630.

120.

160.

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79.3

100.

766

0.7

46

35A

DF

-0.0

8-0

.20

-0.1

10.

610.

630.

150.

160.

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92.4

130.

744

0.7

23

36A

EF

-0.0

8-0

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780.

540.

130.

160.

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74.6

890.

765

0.7

45

37B

CF

-0.1

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-0.0

80.

780.

630.

140.

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81.3

290.

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0.7

39

38B

DF

-0.1

0-0

.17

-0.1

10.

610.

630.

180.

160.

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67.0

660.

774

0.7

55

39B

EF

-0.1

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.17

-0.1

10.

780.

540.

160.

160.

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27.0

910.

736

0.7

15

40C

DF

-0.1

0-0

.20

-0.0

80.

600.

630.

130.

160.

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700.

758

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38

41C

EF

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80.

780.

550.

120.

160.

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090.

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30

42D

EF

-0.1

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610.

540.

150.

160.

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01.7

460.

767

0.7

47

125 6.4. Experimental design: estimation and resultsS

Pa

SV

bP

aram

eter

esti

mat

esF

itst

atis

tics

η PARSER

η CONALC

η SUSP

η DLAB

η COMTOT

λρ1

ρ2

Log

-li.

R2 1c

R2 2d

43A

BC

D-0

.61

-0.3

1-0

.16

0.63

0.28

-0.3

60.

300.

17-4

22.4

740.

736

0.7

14

44A

BC

E-0

.60

-0.3

1-0

.16

0.81

0.20

-0.3

50.

300.

17-3

29.1

130.

727

0.7

05

45B

CD

E-0

.63

-0.3

1-0

.16

0.63

0.20

-0.3

50.

300.

1731

4.84

70.

744

0.7

22

46A

CD

E-0

.60

-0.3

4-0

.16

0.63

0.20

-0.3

30.

300.

17-3

11.3

920.

750

0.7

29

47A

BC

F-0

.08

-0.1

7-0

.08

0.78

0.63

0.15

0.16

0.25

-297

.127

0.76

50.7

46

48A

BD

F-0

.08

-0.1

7-0

.11

0.61

0.63

0.19

0.16

0.25

-203

.763

0.76

10.7

41

49A

BE

F-0

.08

-0.1

7-0

.11

0.78

0.54

0.17

0.16

0.25

-457

.153

0.72

80.7

06

50A

CD

F-0

.08

-0.2

0-0

.08

0.60

0.63

0.14

0.16

0.25

-363

.791

0.71

80.6

95

51A

DE

F-0

.08

-0.2

0-0

.11

0.61

0.54

0.16

0.16

0.25

-349

.525

0.73

60.7

14

52A

CE

F-0

.08

-0.2

0-0

.08

0.78

0.55

0.12

0.16

0.25

-346

.072

0.74

20.7

20

53B

CD

F-0

.10

-0.1

7-0

.08

0.61

0.63

0.17

0.16

0.25

-238

.443

0.75

30.7

33

54B

CE

F-0

.10

-0.1

7-0

.08

0.78

0.55

0.15

0.16

0.25

-331

.808

0.75

80.7

38

55B

DE

F-0

.10

-0.1

7-0

.11

0.61

0.54

0.19

0.16

0.25

359.

178

0.71

80.6

94

56C

DE

F-0

.10

-0.2

0-0

.08

0.61

0.54

0.14

0.16

0.25

-344

.910

0.73

50.7

13

57A

BD

E-0

.60

-0.3

1-0

.19

0.64

0.19

-0.3

50.

300.

16-2

51.5

440.

728

0.7

05

58A

BC

DE

-0.6

0-0

.31

-0.1

60.

630.

20-0

.35

0.30

0.17

-233

.828

0.75

10.7

30

59A

BC

DF

-0.0

8-0

.17

-0.0

80.

610.

630.

170.

160.

25-3

93.8

560.

708

0.6

84

60A

BC

EF

-0.0

8-0

.17

-0.0

80.

780.

550.

160.

160.

25-3

79.5

900.

726

0.7

04

61B

CD

EF

-0.1

0-0

.17

-0.0

80.

610.

540.

180.

160.

25-2

81.6

110.

717

0.6

93

62A

CD

EF

-0.0

8-0

.20

-0.0

80.

610.

540.

140.

160.

25-2

68.5

080.

743

0.7

22

63A

BD

EF

-0.0

8-0

.17

-0.1

10.

610.

540.

200.

160.

25-2

68.5

080.

743

0.7

22


SPa

SV

bP

aram

eter

esti

mat

esF

itst

atis

tics

η PARSER

η CONALC

η SUSP

η DLAB

η COMTOT

λρ1

ρ2

Log

-li.

R2 1c

R2 2d

64A

BC

DE

F-0

.08

-0.1

7-0

.08

0.61

0.54

0.18

0.16

0.25

-316

.290

0.70

70.6

83

Table

6.7

:D

RA

Ges

tim

atio

n.

aSample

path

sgenera

ted

by

UCM

.

bSourceofvariation.

cR

2 1−

Pse

udo-R

2.

dR

2 2−

Adju

sted

pse

udo-R

2.


6.4.2 Generating UCM samples

The 26 UCM samples were generated using the Matlab package. As mentionedabove, since there are no replications, a single observation was generated foreach combination, thus resulting 26 = 64 sample paths (realization- timeseries) (Figure 6.3).

As mentioned earlier each UCM sample path was generated using equa-tions (3.12)-(3.14), with the I and II level values of parameters, δPARSER ={−0.24,−0.19}, δCONALC = {−0.38,−0.30}, δSUSP = {−0.31,−0.24}, δDLAB ={2.03, 1.62}, δCOMTOT = {0.97, 0.77} and σ2

ζ = {0.020, 0.025} (Table 6.3).The parameters δRPC and σ2

ε were kept constant. The simulation was carriedout with the estimated value of σ2

ε = 0.05 (see Section 6.3.2). The estimateof δRPC was defined to be equal to, δRPC = −0.15, based on the results of theprevious work on this variable (see Dadashova et al. (2014)).

6.4.3 Estimating DRAG models using the UCM sam-

ples

One layer DRAG models (Liem et al. , 2008), accident frequency, were builtusing the TRIO software. The number of independent variables included inthe models are the same as the simulated UCM (equation (6.2)-(6.4)), i.e.COMTOT , CONALC, SUSP , PARSER, DLAB and RPC. Taking theindependent variables into account, the BCT structure and the autoregres-sive order of error term are determined next. The optimization is carried outthrough the Davidon-Fletcher (DFP) algorithm, which allows for the max-imization of all the parameters simultaneously. It was found out that withthe same BCT value for both dependent and independent variables and ARstructure of order, l = 2, DRAG models achieved the best goodness of fit mea-sures, i.e. pseudo-R2 measures, log likelihood and conditional t−statistics ofparameters (see Appendix VI). The model estimation was carried out for 64time series, with each having 120 simulated observations.

The results of the DRAG modeling show that DRAG models do notseem to suffer from the absence of a specific trend term, i.e., the three classesof parameters: regression coefficients (estimates and elasticity), BCT coeffi-cients and autoregressive parameters provide a reasonable explanation of thedata generating process as quantified by pseudo-R2 and t- statistic signifi-cance tests for the independent variables. More precisely, the pseudo-R2 for64 models range around 70% to 90%, the BCT, AR coefficients and regres-sor estimates are statistically significant. Since the DRAG model regressors


6.3.a

6.3.b

Fig. 6.3. Generated samples

6.3.a) σ2ζ = 0.020; 6.3.b) σ2ζ = 0.025.


are explained by the elasticities (equation 3.43) rather than by the regres-sor estimates themselves, the parameters of interest of DRAG model are theelasticities of 5 regressors: ηPARSER, ηCONALC , ηSUSP , ηDLAB, and ηCOMTOT ;BCT coefficient, λ, and two autoregressive parameters, ρ1 and ρ2, thus sum-ming up to 8 response variables. The results of DRAG estimation togetherwith the goodness of fit statistics are reported in Table 6.7.

6.4.4 ANOVA

The ANOVAs (Montgomery , 2000, Pena , 1987) of the eight responses werecarried out to quantify on average the individual (main effects) and joint (in-teractions) effects of the inputs (UCM parameters) on the outputs (DRAGestimates). Each of the eight ANOVA’s corresponds to a different DRAGparameter, thus each of the eight variance analysis were carried out inde-pendently. The relative importance of main effect or interaction is givenindistinctly by its factor estimates, sum of squares or F -statistics. Here wehave shown interactions up to fourth order, and used sums of squares of 5th

and 6th order as residual variance. It should be pointed out that, given thespecial nature of computer experiments this choice is slightly arbitrary andof not much relevance. The significance of the factors is based on the sumsof squares, thus the higher order interactions that are not significant can beneglected, since they do not contribute any additional value to the results ofthe experimental design study.

6.4.5 Results of the experimental design-ANOVA

The most significant effects for each of the eight responses are reported in Ta-ble 6.8 (see Appendix VII). Reviewing the results we can observe the followingsimilar behavior among them:

1. The corresponding UCM variable coefficient (elasticity) is a very signif-icant factor for all of the regressor elasticities.

2. The trend component variance, σ2ζt

of UCM is the one of the two mostsignificant factors for all of the parameters.

Item (1) implies that, the elasticities capture partially the true effect ofthe given variable, while (2) shows that the stochastic trend component (F ),if present in the real data, will be captured mainly by the regressor elasticities(strong factor effect).


Table 6.8: Significant main effects for DRAG parameters.

DRAG UCM Effect Sum Mean D.F. F test Pr(>F) Percentage

Parameter Factors Estimates Squares Square Contribution

ηPARSER

F 0.5230 4. 3759 4. 3759 1 7. 19E+05 < 2. 20E-16 99. 822

A 0.0216 0. 0075 0. 0075 1 1. 23E+03 4. 03E-09 0. 171

ηCONALC

F 0.1399 0. 31332 0. 31332 1 16734. 3095 4. 35E-13 94. 543

B 0.0326 0. 017096 0. 017096 1 913. 0677 1. 12E-08 5. 159

ηSUSP

F 0.0274 0. 099146 0. 099146 1 6345361 < 2. 20E-16 89. 097

C 0.0787 0. 012018 0. 012018 1 769129 2. 20E-16 10. 800

ηDLAB

D -0.1757 0. 49386 0. 49386 1 2. 13E+06 < 2. 20E-16 97. 251

F -0.0292 0. 01363 0. 01363 1 5. 87E+04 5. 38E-15 2. 684

ηCOMTOT

F 0.3433 1. 88582 1. 88582 1 19405. 6728 2. 59E-13 94. 331

E -0.0818 0. 10709 0. 10709 1 1102. 0183 5. 83E-09 5. 357

ρ1

F -0.1464 0. 34325 0. 34325 1 1. 03E+07 < 2. 20E-16 99. 997

ρ2

F 0.3065 0. 103765 0. 103765 1 6. 55E+05 < 2. 20E-16 99. 897

λ

F 0.4886 3. 7893 3. 7893 1 3. 25E+05 < 2. 20E-16 99. 491

For example, the standard expression of the model for the 2k design inthe case of the DRAG parameter ηDLAB (DRAG model elasticity of variableDLAB), only including significant main effects and interactions (p−value<0.0001) is as follows:

ηDLAB = c+D

2XD +

F

2XF +

DF

2XDXF +

C

2XC+

+B

2XB +

EF

2XEXF +

CE

2XCXE (6.5)

where c is the average response, D, F , etc. are the effect estimates and XD,XF , etc. are the contrast coefficients taking values (−1) and (+1) describingfactor Levels I and II respectively. For example, equation (6.6) correspondsto the (-1) level of all factors included as significant in the model:

ηDLAB = 0.7074 +−0.1757

2(−1) +

−0.0292

2(−1) +

0.0013

2(−1)(−1)+

+−0.0023

2(−1) +

0.0019

2(−1) +

0.0157

2(−1)(−1)+

+0.0003

2(−1)(−1) = 0.8173 (6.6)


Fig. 6.4. Interaction plot between D and F , for the DRAG parameter ηDLAB .

In accordance with the standard parameterization of 2k designs, whenfactor D changes its value from Level I to Level II (i.e., from 2.03 to 1.62in Table 6.3) the average response decreases by 0.1757. This main effect isof course an average over the remaining factors. However, the presence ofsignificant interactions is also worth interpreting. For example, a significantinteraction between D and F for this response (ηDLAB), indicates that theeffect of D on the response depends on the value taken by F (Figure 6.4). Ascan be seen in Table 6.12, this interaction is the most significant factor aftermain effects D and F .

In Table 6.8, one can observe that for those responses that 1) are relatedto the effect of the variables on the time series, i.e, PARSER, CONALC,SUSP , and COMTOT ; and 2) the main effect of trend is positive, then thetrend is the most significant factor and accounts for 99%, 94%, 89%, and94% of total variability in PARSER, CONALC, SUSP , and COMTOTrespectively. On the other hand, for the ηDLAB, the effect of trend is negativeand the trend is the second most significant main effect, accounting for 2.68%of the total response variability. The effect of the corresponding UCM factor


for DLAB, D, accounts for 97.25% of variability in this case. The resultsin general show that the sensitivity of elasticity estimators to the changes instochastic trend variance is significantly high.

Thus, the regressor elasticities of the DRAG models do not only repre-sent the effect of the independent variables but also pick up the trend variancepresent in the data. The autoregressive error structure of the DRAG modelcan partially pick up the effect of the trend, i.e. the stochastic trend presentin the data is picked up both by regressors and the autoregressive error.


It is true that the results of the estimation can differ depending on the typeof model used. However the question is how significant is this difference? Ananalytical quantification of the differences between the two types of models,e.g. explanatory and descriptive models is an almost unfeasible process. Thischapter tries to answer this question using existing statistical tools, MonteCarlo simulation, experimental design and ANOVA. The main idea is how agiven model can be interpreted through another. This approach shows howthe parameters of two different classes of models: DRAG and UCM, capturethe effect of an unobserved stochastic component that can be present in thedata.

As it was indicated the final results of experimental design using thesimulated data show that:

1. The regressor elasticities of DRAG model are capturing the change inthe corresponding UCM elasticities as it was initially assumed.

2. The stochastic trend component of UCM was not only captured by theautoregressive parameters of the DRAG model but also by the regressorelasticity parameters.

The results reveal some interesting aspects on that could be overlookedduring the model selection process. This research work shows how a misspec-ification of the stochastic component present in true data generating processcan lead to biased estimates and thus to erroneous interpretation. Also, thatthe stochastic trend component has the most significant effect on the re-gression elasticity estimates of the model used for estimation. Although theregressor estimates capture the true effect of the variables, they are moresensitive to changes in the stochastic trend component present in the truedata.


The findings show that, although the goodness of fit measures can pro-vide reliable information, the stochastic component in the data should behandled and adjusted properly in order to provide unbiased estimates. Thisis a very important issue specially in case of road accident modelling sinceone of the main purposes of any road accident modelling is to identify thefactors that have significant impact on accidents. One way of prior fitting isdifferencing the data before estimation. For this purpose the right integrationorder of the data should be determined. However the integration order canbe affected when introducing the explanatory factors, specially if there is alagged relationship between output and input. Future research will be carriedout considering these findings and problems that can be encountered duringthe modelling process.

Part III

Conclusions

135

Conclusions

This thesis has been developed with the purpose of studying the road safetyfactors in Spain during the period 2000-2011, and analyzing the impact ofi.a., policy measures and economic factors. The findings, main contributionsand future work in this direction are presented below.

Contribution

The thesis has both empirical and theoretical contributions to the road safetyliterature that can be presented in several blocks:

1. The first contribution of the thesis is the comparison of two macro mod-els: demand for road use, accidents and their gravity, and unobservedcomponents model. Although there are numerous articles written on theperformance of the models, however a systematic comparison of thesemodels and their ability to interpret and predict the traffic accidentmeasures has not been addressed previously. The study was carriedout using the database on frequency and severity of van-involved roadaccidents in Spain during 2000-2011 and has the following findings andcontributions:

1.1 Structural explanatory models (DRAG type models) prove to be quiteadjustable to the traffic data and provide better predictions than struc-tural descriptive models (unobserved components model). But UC mod-els capture the seasonality in the predicted data more efficiently, mainlydue to the fact that the terms such as trend and seasonality are sep-arately modeled in UCM. The goodness of fit of the model shows it-self strongly in prediction accuracy. In the descriptive models a bettergoodness of fit is achieved when the variables included in the modelare statistically significant. This means that the variables with highest

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p-values should be eliminated (stepwise elimination). The advantage ofthis is that, since stepwise elimination is employed during the model se-lection process, we obtain a rather small set of candidate models, amongwhich it is quite trivial to choose the best one. This however is not veryefficient if the analyst intends to assess the effect of several variables.

1.2 Unlike the descriptive models the explanatory models are very parsi-monious and thus the number of candidate models can be very large.Although this provides a better prediction accuracy compared to the de-scriptive models, selecting the most appropriate model can be a lengthyprocess, since the explanatory models employed in road safety analysisnot only differ in the explanatory variables but also include differentparameters. The examples include the variable transformation param-eter or the parameters associated with the error structure of the model,since it has been shown in different studies that the error term of themodels employed in road safety should not be considered as Gaussian.

1.4 The explanatory models can provide better predictions and prove to bevery useful tool for modeling traffic accident data, allowing to evaluatethe effect of different factors on road safety indicators. These modelshowever lack the ability to capture the unobserved components suchas trend and seasonality that might be present in accident data. Theresults of the experimental design prove this point and it was shown thata term like the stochastic trend which is present in data is captured bythe parameters such as elasticities or even the parameters associatedwith the error term. However they do succeed when estimating the realeffect of the respective factor.

1.5 The results suggest that the fatality measures, number of fatal accidentsand the number of deaths in van-involved accidents are influenced by thesame factors, within each type of model (DRAG or UCM). According toDRAG estimation, all of the explanatory variables categories are presentin models for both indicators. The most significant factors in case ofDRAG estimation belong to the following categories: exposure, driverbehavior surveillance, economic factors and legislative measures. UCMestimation, however, includes relatively few significant factors. Thefactors that are common to these two indicators belong to the followingcategories: exposure (COMTOT), economic activity (PARSER), driversurveillance (CONALC) and calendar effect (DLAB and SDF). It canbe observed that, when the same factor appears both in DRAG and

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UCM, the elasticity estimates are nearly the same, with the exceptionof DLAB.

1.6 Injury- related measures, number of accidents with injuries and num-ber of injured victims in van-involved accidents are affected by the samefactors, within each methodology (DRAG and UCM). Moreover, by an-alyzing the results, it can be concluded that the factors are almostcommon for both methodologies. The most significant variables belongto the following categories: driver behavior surveillance, economic fac-tors and road infrastructure. The variables with significant estimatesgenerally have similar elasticities for both methodologies.

2. The second most important contribution of the thesis is the model se-lection methodology proposed for the macro analysis of road safety in-dicators. Analyzing every possible combination of the parameters andexplanatory factors can be a very lengthy and unfeasible process. Thisstudy was carried out with the purpose of providing an efficient way ofmodel selection. The estimation is carried out within Bayesian frame-work and a parsimonious time series model is used. The study wascarried out using the data on total fatal accidents in Spain for the pe-riod of 2000-2011. The most important findings and contributions ofthe study are:

2.1 The methodology is applied to a parsimonious model. The results of theBayesian estimation do not contradict the results obtained in previousempirical studies on road safety analysis. This is shown in goodness offit measures, prediction accuracy and interpretability of the results.

2.2 The comparison with a fully specified DR model shows that the resultsof the model selection procedure, as far as the estimation and predictionare concerned, are valid.

2.3 The results of variable selection show that inputs such as economicfactors, and legislative and surveillance measures have played significantroles in decreasing the number of fatal accidents during the last decade.These findings agree with the previous assumptions that the changes inthis road safety indicator could be attributed to the improving policymeasures and changing economic situation in the country.

3. The other major contribution of the thesis is the simulation-based method-ology for the model comparison. The main contributions and findingsof this study are:

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3.1 It is true that the estimation results can differ depending on the typeof model used. However, the question is how significant is this differ-ence? An analytical quantification of the differences between two typesof models, e.g. explanatory and descriptive models, is an almost unfea-sible process and requires excessive mathematical computations. Thisstudy tries to answer this question using Monte Carlo simulation, ex-perimental design and ANOVA. The main idea is how a certain modelcan be interpreted through another model.

3.2 The results reveal some interesting aspects on traffic accident researchwhich can be overlooked during the model choice process. This studyshows how a misspecification of the stochastic component present inthe true data generating process, can lead to biased estimates and thusto different interpretation. The results show that the stochastic trendcomponent has the most significant effect on the regression elasticityestimates of the model used for estimation. Although the regressorestimates capture the true effect of the variables, these estimates aremore sensitive to the stochastic trend component present in the data.

3.3 The findings show that although the goodness of fit measures can pro-vide a reliable information the stochastic component in the data shouldbe handled properly in order to provide unbiased estimates. Speciallybearing in mind that the ultimate goal of any road accident model is toidentify the factors that have significant impact on the traffic accidentsthis point has to be dealt with carefully.

Future work

The future empirical and theoretical research will be undertaken followingthe main achievements and contributions of the thesis. The possible lines ofthe future work include:

• Improvement of the TIM selection methodology by including more inputvariables rather than only two inputs. Inclusion of only two inputs cansometimes result in selection of non-optimal variable if the variables arehighly correlated. In order to avoid this problem the variable selectionmethodology, TIM, will be extended to include three or four variables.

• Improvement of the model selection methodology by building sophis-ticated models, i.e. higher autoregressive error structure, more power

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transformation values, etc. This will result in a larger number of modelsto be estimated but will increase the probability of defining the mostlikely model. Given that this process is time consuming and needs morecomputational means the colloboration with the Supercomputing andVisualization Center of Madrid (CeSViMa) and the Spanish Supercom-puting Network (RES) for this purpose is already under way.

• Introducing unobserved components to the basic structural explanatorymodel structure, e.g. SE models with a seasonal autoregressive errorinstead of regular autoregressive errors. Considering that the accidentdata is monthly, it is expected that the seasonality will be present formost of the road safety indicators. The main challenge will be selectionof the right priors for the AR parameters.

• Treatment of stochastic trend component present in the true data byfiltering out the stochastic component. In this case the dependent vari-ables with a stochastic trend will be differenced before the modellingprocess. As it was found out during the experimental design study ifnot handled properly the presence of the stochastic trend could resultin biased estimates and thus in misinterpretation of the variable effects.This research work could be carried out in two directions: 1. theo-retical analysis through simulation study; 2. empirical analysis withthe observed data. The main purpose of the former research will beto test if the prior adjustment of data through differencing can resultin unbiased estimates. For this purpose the new data samples withthe stochastic trend will be generated through SE. The generated datawill be differenced and the UCM estimation will be carried out bothfor the data with the stochastic trend and the differenced data. Theinterpretation of one model through another will be carried out usingvariance analysis as before. Its expected that in case of the differenceddata the effect of the trend variance on the variable estimates shouldbe smaller or non-existent. The second study will consist of the modelselection procedure for the data with a stochastic component. In thisstudy the original data with the stochastic trend will be differenced andthe model selection procedure will be applied to both the original andthe differenced data.

• Application of the methodologies developed in this thesis to differentindicators depicting the road accident frequency and severity in othertypes of vehicles, e.g. trucks, motorcycles, etc. This will help to definehow different factors may affect to different road safety indicators.

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155

Appendix I: DRAG Estimation

=========================================================================================

I. ELASTICITY S(y) (EP) TYPE = LEVEL-1 LEVEL-1 LEVEL-1 LEVEL-1

VARIANT = ACCMOR3 MORHER2 MUER2 HERGRA2

(COND. T-STATISTIC) VERSION = 109 74 134 95

DEP.VAR. = accmor morher muer hergra

=========================================================================================

--------------------------

FLEET CHARACTERISTICS

--------------------------

PRQAB -.721 -.406

(-1.92) (-1.19)

LAM 1 LAM 1

-----

CLIMATOLOGY

-----

DNIE .151 .006 .175

---- (2.47) (.56) (3.39)

SLNV -.162 -.225

---- (-1.75) (-3.02)

TEMP -.002

(-.02)

LAM 1

----------

LABOR

----------

DLAB .670 1.911 .380

(1.09) (1.88) (1.20)

LAM 1 LAM 1 LAM 1

SDF .017 .489

(.18) (1.29)

LAM 1 LAM 1

=========================================================================================





=========================================================================================

---

ROAD INFRASTRUCTURE

---

LONRAC -.375

(-.83)

LAM 1

LONRED -1.485 -1.064 -2.192

(-1.62) (-3.27) (-2.25)

LAM 1 LAM 1 LAM 2

CONST -.866 -1.638

(-2.79) (-3.91)

LAM 1 LAM 1

-----

LEGISLATION

-----

PPS -.100 -.294

=== (-.91) (-2.30)

RPC -.152 -.333 -.111

=== (-2.47) (-4.41) (-1.02)

RUIDO -.008

(-.33)

LAM 1

-------

ECONOMIC FACTORS

-------

IPI .315

(.73)

LAM 1

INDVEN .129 .127

(1.83) (1.18)

LAM 1 LAM 1

INDCOM .612

(1.17)

LAM 1

PRCOM -.044 -.095 -.289

(-.11) (-.54) (-.61)

LAM 1 LAM 1 LAM 1

INDACT 2.114 1.856

(.75) (.65)

LAM 1 LAM 1

PARO -.510 -.338

(-1.99) (-.87)

LAM 1 LAM 1

=========================================================================================





=========================================================================================

-----------------------

SUREILLANCE

-----------------------

CONALC -.172 -.051 -.067 -.118

(-1.09) (-.72) (-.36) (-1.04)


PRADAR -.963

(-2.42)

LAM 1

RADAR -.190 -.025 -.530 -.087

(-1.16) (-.38) (-2.44) (-.98)


PRLSUSP -.262 -.454

(-1.11) (-2.11)

LAM 1 LAM 1

SUSP -.117 -.302

(-1.06) (-1.86)

LAM 1 LAM 1

-----------

EXPOSURE

-----------

PRGFUR 2.290 3.813

(1.50) (2.19)

LAM 1 LAM 1

CNSOIL .772 .145

(1.26) (.16)

LAM 1 LAM 1

COMTOT 1.195 1.137

(4.44) (3.65)

LAM 1 LAM 1

VKM .382

(1.20)

LAM 1

REGRESSION CONSTANT CONSTANT - - - -

(-1.34) (3.02) (-.89) (1.25)

=========================================================================================

II. PARAMETERS TYPE = LEVEL-1 LEVEL-1 LEVEL-1 LEVEL-1




=========================================================================================

------------------------------------------------------------------

BOX-COX TRANSFORMATIONS: UNCOND: [T-STATISTIC=0] / [T-STATISTIC=1]

------------------------------------------------------------------

LAMBDA(Y) hergra -.019

[-.03]

[-1.65]

LAMBDA(Y) - GROUP 1 LAM 1 .168 .067 -.084

[.38] [.15] [-.20]

[-1.86] [-2.12] [-2.54]

LAMBDA(X) - GROUP 1 LAM 1 .168 .067 -.084 -.373

[.38] [.15] [-.20] [-.35]

[-1.86] [-2.12] [-2.54] [-1.28]

LAMBDA(X) - GROUP 2 LAM 2 -.196

[-.06]

[-.38]

=========================================================================================

II. PARAMETERS TYPE = LEVEL-1 LEVEL-1 LEVEL-1 LEVEL-1




=========================================================================================

---------------

AUTOCORRELATION

---------------

ORDER 1 RHO 1 -.324 -.485 .103

(-2.46) (-3.16) (.81)

ORDER 2 RHO 2 -.275 .058 -.315 -.020

(-2.30) (.48) (-2.19) (-.19)

ORDER 3 RHO 3 -.128 .061 -.107 .062

(-.86) (.48) (-.76) (.46)

ORDER 4 RHO 4 -.248 .193 -.210 .150

(-1.84) (1.38) (-1.56) (1.17)

ORDER 5 RHO 5 .117 .042

(.98) (.39)

ORDER 6 RHO 6 .037 .198

(.26) (1.89)

ORDER 7 RHO 7 -.043 -.076

(-.36) (-.65)

ORDER 8 RHO 8 .138 .189

(1.12) (1.52)

ORDER 9 RHO 9 -.095 -.206

(-.68) (-1.86)

ORDER 10 RHO 10 -.268 -.261

(-2.43) (-2.48)

ORDER 11 RHO 11 -.035 -.097

(-.29) (-.84)

ORDER 12 RHO 12 -.020 .000

(-.16) (.00)

ORDER 14 RHO 14 -.186 -.206

(-1.36) (-1.76)

=========================================================================================

III.GENERAL STATISTICS TYPE = LEVEL-1 LEVEL-1 LEVEL-1 LEVEL-1


VERSION = 109 74 134 95


=========================================================================================

LOG-LIKELIHOOD -309.861 -368.933 -333.696 -409.788

PSEUDO-R2 : - (E) .578 .785 .576 .729

- (L) .595 .795 .625 .750

- (E) ADJUSTED FOR D.F. .463 .714 .440 .630

- (L) ADJUSTED FOR D.F. .486 .728 .505 .658

AVERAGE PROBABILITY (Y=LIMIT OBSERV.) .000 .000 .000 .000

SAMPLE : - NUMBER OF OBSERVATIONS 104 94 104 94

- FIRST OBSERVATION 5 15 5 15

- LAST OBSERVATION 108 108 108 108

NUMBER OF ESTIMATED PARAMETERS :

- FIXED PART :

. BETAS 18 11 20 11

. BOX-COX 1 1 2 2

. ASSOCIATED DUMMIES 0 0 0 0

- AUTOCORRELATION 4 12 4 13

- HETEROSKEDASTICITY :

. DELTAS 0 0 0 0

. BOX-COX 0 0 0 0

. ASSOCIATED DUMMIES 0 0 0 0

=========================================================================================

Appendix II: UCM Estimation

The SAS System

The UCM Procedure

Input Data Set

Name UCMFURGO.ACCMOR

Time ID Variable DATE

Estimation Span Summary

First Last Standard

Variable Type Obs Obs NObs NMiss Min Max Mean Deviation

ACCMOR Dependent JAN2000 DEC2009 120 0 2.48491 4.02535 3.36946 0.28973

x24 Predictor JAN2000 DEC2009 120 0 8.86954 9.82831 9.44891 0.25055

X36 Predictor JAN2000 DEC2009 120 0 7.51833 7.98036 7.79684 0.09299



CONALC Predictor JAN2000 DEC2009 120 0 11.60084 13.27341 12.25503 0.44519


Forecast Span Summary

First Last Standard


ACCMOR Dependent JAN2000 DEC2008 108 0 2.83321 4.02535 3.42113 0.24571





CONALC Predictor JAN2000 DEC2009 120 0 11.60084 13.27341 12.25503 0.44519


Preliminary Estimates of the Free Parameters

Component Parameter Estimate

Irregular Error Variance 0.02467

Likelihood Based Fit Statistics

Statistic Value


Diffuse Part of Log Likelihood 6.9992

Non-Missing Observations Used 120

Estimated Parameters 1

Initialized Diffuse State Elements 6

Normalized Residual Sum of Squares 114

The SAS System

The UCM Procedure


Statistic Value



AICC (smaller is better) -47.58

HQIC (smaller is better) -46.5

CAIC (smaller is better) -43.88

Final Estimates of the Free Parameters

Approx Approx

Component Parameter Estimate Std Error t Value Pr > |t|

Irregular Error Variance 0.03247 0.0043003 7.55 <.0001

SUSP Coefficient -0.31080 0.11805 -2.63 0.0085

COMTOT Coefficient 0.97622 0.22713 4.30 <.0001

DLAB Coefficient 2.03588 0.47335 4.30 <.0001

SDF Coefficient 0.07559 0.02179 3.47 0.0005

CONALC Coefficient -0.38317 0.05612 -6.83 <.0001

PARSER Coefficient -0.24949 0.10274 -2.43 0.0152

Fit Statistics Based on Residuals

Mean Squared Error 0.15874

Root Mean Squared Error 0.39842

Mean Absolute Percentage Error 5.66279

Maximum Percent Error 91.67443

R-Square -0.85276

Adjusted R-Square -0.85276

Random Walk R-Square -0.72931

Amemiya’s Adjusted R-Square -0.88555

Number of non-missing residuals used for

computing the fit statistics = 114

The UCM Procedure

Significance Analysis of Components

(Based on the Final State)

Component DF Chi-Square Pr > ChiSq

Irregular 1 11.40 0.0007

Outlier Summary

Standard

Obs DATE Break Type Estimate Error Chi-Square DF Pr > ChiSq

28 APR2002 Additive Outlier -0.57946 0.1826786 10.06 1 0.0015

62 FEB2005 Additive Outlier 0.52371 0.1858743 7.94 1 0.0048

Forecasts for Variable accmorlog

Standard

Obs DATE Forecast Error 95% Confidence Limits

109 JAN2009 2.845549 0.20159 2.450449 3.240649

110 FEB2009 2.795925 0.20825 2.387761 3.204090

111 MAR2009 3.035446 0.19257 2.658023 3.412869

112 APR2009 2.946081 0.19667 2.560614 3.331547

113 MAY2009 2.996205 0.19336 2.617219 3.375190

114 JUN2009 3.010762 0.19570 2.627203 3.394321

115 JUL2009 3.194268 0.18940 2.823046 3.565490

116 AUG2009 2.981562 0.19963 2.590295 3.372829

117 SEP2009 2.959570 0.20199 2.563671 3.355468

118 OCT2009 3.028555 0.19340 2.649500 3.407609

119 NOV2009 2.864803 0.20304 2.466857 3.262748

120 DEC2009 2.989988 0.19893 2.600099 3.379878

Post Sample Predictions for accmorlog

Sum of Sum of

Prediction Squared Absolute

Obs DATE Actual Forecast Error Errors Errors

109 JAN2009 2.708050201 2.845549196 -0.13749899 0.018905973 0.137498995

110 FEB2009 2.708050201 2.795925238 -0.08787504 0.026627996 0.225374031

111 MAR2009 3.258096538 3.035446363 0.222650175 0.076201096 0.448024206

112 APR2009 2.48490665 2.94608071 -0.46117406 0.288882609 0.909198266

113 MAY2009 3.091042453 2.996204641 0.094837813 0.29787682 1.004036078

114 JUN2009 2.890371758 3.010762128 -0.12039037 0.312370661 1.124426448

115 JUL2009 3.044522438 3.194267706 -0.14974527 0.334794307 1.274171717

116 AUG2009 3.218875825 2.981561909 0.237313916 0.391112201 1.511485633

117 SEP2009 2.833213344 2.959569572 -0.12635623 0.407078098 1.63784186

The SAS System 15:07 Wednesday, October 12, 2011

The UCM Procedure

Post Sample Predictions for accmorlog

Sum of Sum of



118 OCT2009 3.135494216 3.028554665 0.106939551 0.418514165 1.744781411

119 NOV2009 2.708050201 2.864802551 -0.15675235 0.443085464 1.901533761

120 DEC2009 2.772588722 2.989988266 -0.21739954 0.490348026 2.118933304

The SAS System

The UCM Procedure

Input Data Set

Name UCMFURGO.MORHER



First Last Standard


MORHERlog Dependent JAN2000 DEC2009 120 0 4.43082 5.47646 5.09374 0.21659









First Last Standard


MORHERlog Dependent JAN2000 DEC2008 108 0 4.63473 5.47646 5.14318 0.16164








Fixed Parameters in the Model

Component Parameter Value

Season Error Variance 0

The SAS System

The UCM Procedure





Statistic Value













Approx Approx



PARO Coefficient -0.21785 0.06804 -3.20 0.0014

INDACT Coefficient 1.63687 0.65715 2.49 0.0127

AIRBAG Coefficient -0.15995 0.04038 -3.96 <.0001

PRLSUSP Coefficient -0.16287 0.08228 -1.98 0.0478

LONRED Coefficient -1.61663 0.21602 -7.48 <.0001


SDF Coefficient 0.01833 0.01002 1.83 0.0675






R-Square 0.69391



The SAS System

The UCM Procedure


Adjusted R-Square 0.69391

Random Walk R-Square 0.21988

Amemiya’s Adjusted R-Square 0.68785






Irregular 1 11.40 0.0007

Season 11 29.60 0.0018

Summary of Seasons

Season Error

Name Type Length Variance

Season TRIG 12 0

Outlier Summary

Standard


1 JAN2000 Additive Outlier 0.21977 0.0928905 5.60 1 0.0180

75 MAR2006 Additive Outlier 0.19197 0.08796 4.76 1 0.0291

Forecasts for Variable MORHERlog

Standard


109 JAN2009 4.610003 0.09892 4.416125 4.803880

110 FEB2009 4.560335 0.10161 4.361179 4.759491

111 MAR2009 4.592575 0.10479 4.387181 4.797969

112 APR2009 4.539348 0.11205 4.319736 4.758960

113 MAY2009 4.576851 0.11445 4.352536 4.801166

114 JUN2009 4.678371 0.11541 4.452170 4.904571

115 JUL2009 4.768373 0.11642 4.540202 4.996544

116 AUG2009 4.598594 0.11563 4.371972 4.825217

117 SEP2009 4.509347 0.11562 4.282735 4.735959

118 OCT2009 4.646332 0.12262 4.406004 4.886661

The SAS System

The UCM Procedure

Forecasts for Variable MORHERlog

Standard


119 NOV2009 4.498467 0.11589 4.271327 4.725608

120 DEC2009 4.502763 0.12009 4.267399 4.738128

Post Sample Predictions for MORHERlog

Sum of Sum of



109 JAN2009 4.574710979 4.610002608 -0.03529163 0.001245499 0.03529163

110 FEB2009 4.510859507 4.560335128 -0.04947562 0.003693336 0.084767251

111 MAR2009 4.779123493 4.592575057 0.186548436 0.038493655 0.271315688

112 APR2009 4.624972813 4.539348008 0.085624805 0.045825263 0.356940493

113 MAY2009 4.744932128 4.57685125 0.168080879 0.074076444 0.525021372

114 JUN2009 4.744932128 4.678370594 0.066561534 0.078506882 0.591582906

115 JUL2009 4.804021045 4.768372955 0.035648089 0.079777669 0.627230995

116 AUG2009 4.663439094 4.598594136 0.064844958 0.083982537 0.692075953

117 SEP2009 4.430816799 4.509346825 -0.07853003 0.090149502 0.770605979

118 OCT2009 4.663439094 4.646332317 0.017106777 0.090442144 0.787712757

119 NOV2009 4.543294782 4.498467107 0.044827675 0.092451664 0.832540432

120 DEC2009 4.700480366 4.502763248 0.197717118 0.131543723 1.03025755

The SAS System

The UCM Procedure

Input Data Set

Name UCMFURGO.MUER



First Last Standard


MUERlog Dependent JAN2000 DEC2009 120 0 2.56495 4.17439 3.52044 0.31583


lagx19 Predictor JAN2000 DEC2009 120 0 11.60084 13.27341 12.25503 0.44519





First Last Standard


MUERlog Dependent JAN2000 DEC2008 108 0 2.89037 4.17439 3.57575 0.26781


lagx19 Predictor JAN2000 DEC2009 120 0 11.60084 13.27341 12.25503 0.44519








Statistic Value









The SAS System

The UCM Procedure


Statistic Value





Approx Approx



PARSER Coefficient -0.40790 0.10770 -3.79 0.0002


COMTOT Coefficient 0.73966 0.23849 3.10 0.0019

SDF Coefficient 0.11664 0.02239 5.21 <.0001

DLAB Coefficient 2.62313 0.52146 5.03 <.0001






R-Square 0.41437









Irregular 1 8.33 0.0039

The SAS System

The UCM Procedure

Outlier Summary

Standard


28 APR2002 Additive Outlier -0.68394 0.2138883 10.23 1 0.0014

62 FEB2005 Additive Outlier 0.67209 0.2176265 9.54 1 0.0020

Forecasts for Variable MUERlog

Standard


109 JAN2009 2.998799 0.23595 2.536342 3.461256

110 FEB2009 2.874368 0.24308 2.397936 3.350799

111 MAR2009 3.192832 0.22543 2.750991 3.634674

112 APR2009 3.038320 0.22961 2.588287 3.488352

113 MAY2009 3.176286 0.22604 2.733256 3.619317

114 JUN2009 3.075144 0.22771 2.628836 3.521453

115 JUL2009 3.263243 0.22022 2.831611 3.694875

116 AUG2009 3.081502 0.23344 2.623971 3.539032

117 SEP2009 3.000561 0.23418 2.541580 3.459542

118 OCT2009 3.162418 0.22650 2.718492 3.606344

119 NOV2009 2.987256 0.23778 2.521214 3.453298

120 DEC2009 3.092564 0.23249 2.636894 3.548234

Post Sample Predictions for MUERlog

Sum of Sum of



109 JAN2009 2.890371758 2.998799075 -0.10842732 0.011756483 0.108427318

110 FEB2009 2.708050201 2.874367583 -0.16631738 0.039417955 0.274744699

111 MAR2009 3.33220451 3.19283247 0.13937204 0.05884252 0.414116739

112 APR2009 2.564949357 3.038319811 -0.47337045 0.282922107 0.887487193

113 MAY2009 3.218875825 3.176286347 0.042589477 0.28473597 0.930076671

114 JUN2009 2.944438979 3.075144413 -0.13070543 0.301819881 1.060782105

115 JUL2009 3.044522438 3.263243185 -0.21872075 0.349658646 1.279502852

116 AUG2009 3.555348061 3.081501689 0.473846373 0.574189031 1.753349225

117 SEP2009 3.091042453 3.000561198 0.090481256 0.582375889 1.843830481

118 OCT2009 3.258096538 3.162417762 0.095678776 0.591530317 1.939509257

119 NOV2009 2.772588722 2.987256097 -0.21466737 0.637612399 2.154176631

120 DEC2009 2.890371758 3.092563779 -0.20219202 0.678494012 2.356368652

The SAS System

The UCM Procedure

Input Data Set

Name UCMFURGO.HERGRA



First Last Standard


HERGRA Dependent JAN2000 DEC2009 120 0 4.57471 5.68358 5.24099 0.25212






x11 Predictor JAN2000 DEC2009 120 0 0 1 0.20833 0.40782


First Last Standard


HERGRA Dependent JAN2000 DEC2009 120 0 4.57471 5.68358 5.24099 0.25212






x11 Predictor JAN2000 DEC2009 120 0 0 1 0.20833 0.40782

Fixed Parameters in the Model


Irregular Error Variance 0

RPC Error Variance 0





Statistic Value

Full Log Likelihood -8.156






AIC (smaller is better) 18.311

BIC (smaller is better) 20.946

The SAS System

The UCM Procedure


Statistic Value

AICC (smaller is better) 18.351

HQIC (smaller is better) 19.379

CAIC (smaller is better) 21.946


Approx Approx


Season Error Variance 0.00068677 0.0000957 7.18 <.0001

PARO Coefficient -0.18544 0.07713 -2.4 0.0162



SUSP Coefficient -0.43721 0.09072 -4.82 <.0001

RUIDO Coefficient -0.05168 0.0154 -3.36 0.0008

RPC Coefficient -0.05596 0.0388 -1.44 0.1493






R-Square 0.3758









Irregular 0 . .

Season 11 38.66 <.0001

Summary of Seasons

Name Type Season Length Error Variance

Season TRIG 12 0.00068677

The SAS System

The UCM Procedure

Outlier Summary

Standard


75 MAR2006 Additive Outlier 0.6893 0.1473719 21.88 1 <.0001

74 FEB2006 Additive Outlier 0.63582 0.1462865 18.89 1 <.0001

Forecasts for Variable HERGRA

Standard


109 JAN2009 4.888183 0.25566 4.387095 5.389271

109 JAN2009 4.785545 0.25839 4.279106 5.291985

111 MAR2009 4.652695 0.25443 4.154012 5.151379

112 APR2009 4.77492 0.25593 4.273314 5.276525

113 MAY2009 4.77492 0.25593 4.273314 5.276525

114 JUN2009 5.09988 0.23237 4.644445 5.555315

115 JUL2009 5.141305 0.25327 4.644913 5.637697

116 AUG2009 4.738095 0.23929 4.26909 5.207101

117 SEP2009 4.713624 0.23978 4.243668 5.18358

118 OCT2009 4.886632 0.23748 4.421171 5.352093

119 NOV2009 4.612448 0.23189 4.157953 5.066943

120 DEC2009 4.834177 0.22969 4.383997 5.284357

Post Sample Predictions for HERGRA

Sum of Sum of



109 JAN2009 4.59511985 4.888182981 -0.29306313 0.085885999 0.293063131

110 FEB2009 4.605170186 4.785545441 -0.18037525 0.118421231 0.473438386

111 MAR2009 4.812184355 4.811209575 0.000974781 0.118422182 0.474413167

112 APR2009 4.744932128 4.652695465 0.092236663 0.126929784 0.56664983

113 MAY2009 4.859812404 4.774919573 0.084892831 0.134136576 0.651542661

114 JUN2009 4.934473933 5.099880127 -0.16540619 0.161495785 0.816948855

115 JUL2009 4.912654886 5.14130519 -0.2286503 0.213776747 1.045599158

116 AUG2009 4.753590191 4.73809548 0.015494711 0.214016833 1.06109387

117 SEP2009 4.574710979 4.713623939 -0.13891296 0.233313643 1.20000683

118 OCT2009 4.682131227 4.886632151 -0.20450092 0.275134271 1.404507754

119 NOV2009 4.59511985 4.612447926 -0.01732808 0.275434534 1.42183583

120 DEC2009 4.820281566 4.834176862 -0.0138953 0.275627613 1.435731126

Appendix III: WinBUGS Codes

WinBugs Code: Structural explanatory model estimation

model {

mu[1] <- inprod( b[], X[1,])

Y[1] ~ dnorm(mu[1],tau.u)

mu[2] <- inprod( b[], X[2,])

+rho[1]*(Y[1]-inprod( b[], X[1,]))

Y[2] ~ dnorm(mu[2],tau.e)

for (t in 3:T){

mu[t] <- inprod( b[], X[t,])

+rho[1]*(Y[t-1]-inprod( b[], X[t-1,]))

+rho[2]*(Y[t-2]-inprod( b[], X[t-2,]))

Y[t] ~ dnorm(mu[t], tau.e)

Y.pred[t]~ dnorm(mu[t], tau.e) #Prediction estimation

}

for (t in T+1:N){

mu.pred[t] <- inprod( b[], X[t,])

+rho[1]*(Y.pred[t-1]-inprod( b[], X[t-1,]))

+rho[2]*(Y.pred[t-2]-inprod( b[], X[t-2,]))

Y.pred[t]~ dnorm(mu.pred[t], tau.e)

}

sigma.e <- 1/tau.e

sigma.u <-sigma.e*(1-rho[2])/((1+rho[2])*(pow((1-rho[2]),2)

-pow(rho[1],2)))

tau.u <- 1/sigma.u

for (i in 1:2) {

rho[i]~ dunif(r0[i], R0[i])

}

b[1:n] ~ dmnorm(b0[], B0[ , ])

tau.e ~ dgamma(0.01, 0.01)

}

DATA

list(’n’,’N’,’T’,’X’,’Y’,’b0’,’B0’,’r0’,’R0’ )

INITS

list( b=c(matrix(data=0.01, nrow=1, ncol=n)),

rho=c(0.05,0.01),tau.e=.01)

Appendix IV: SE Bayesian Estimation: Vari-

able Selection

177

M X1 X2 λX = −0.5 λX = 0.1 λX = 0.5

1 V HP VKM 0.8177146 0.8175842 0.8177526

2 V HP CONGAS 0.8633223 0.8164691 0.8110146

3 V HP PARO 0.854253 0.7985948 0.7977917

4 V HP OCUP1 0.8022488 0.8015802 0.6126772

5 V HP OCUP4 0.7936083 0.8063415 0.6618917

6 V HP PRCRN 0.7604337 0.788923 0.6724536

7 V HP IPI 0.8024817 0.8023117 0.6131628

8 V HP PCONCEM 0.7903066 0.7904969 0.6626231

9 V HP MANT 0.5815363 0.7470997 0.6725995

10 V HP PRECOML 0.8016426 0.8040959 0.8392632

11 V HP PREC 0.8022192 0.7996903 0.7984826

12 V HP HSOL 0.8005376 0.7712959 0.7729773

13 V HP DNIEB 0.802471 0.8186242 0.6133427

14 V HP DLAB 0.7937751 0.8077033 0.6620008

15 V HP COND 0.6985997 0.7623451 0.6727231

16 V HP CONALC 0.8029933 0.8148661 0.6130014

17 V HP RADAR 0.7956255 0.813858 0.6618806

18 V HP SUSP 0.7408465 0.7431765 0.6722548

19 V HP V EH10 0.8200421 0.8123648 0.8166806

20 V HP ABS 0.8365977 0.7980062 0.8124503

21 V HP LONRAC 0.8189307 0.6895311 0.7674998

22 V HP LONRED 0.8023182 0.8035284 0.8195032

23 V HP PPS 0.8154297 0.7952132 0.7994828

24 V HP PCR 0.7908286 0.7205856 0.7315893

25 V HP SDF 0.8018307 0.8031048 0.8148504

26 V HP SEMSAN 0.7948011 0.8041271 0.8201274

27 V HP DSCN 0.7739817 0.7958927 0.8193945

28 V KM CONGAS 0.8042948 0.8029049 0.8149373

29 V KM PARO 0.8010769 0.8003293 0.8291742

30 V KM OCUP1 0.7956938 0.7685242 0.7783732

M X1 X2 λX = −0.5 λX = 0.1 λX = 0.5

31 V KM OCUP4 0.8177369 0.8024944 0.8142447

32 V KM PRCRN 0.8068281 0.7997772 0.799153

33 V KM IPI 0.7281825 0.7443171 0.7457771

34 V KM PCONCEM 0.8150335 0.8019097 0.8158791

35 V KM MANT 0.8110105 0.8525853 0.662618

36 V KM PRECOML 0.7509789 0.8417006 0.6869132

37 V KM PREC 0.8122344 0.8016743 0.8158597

38 V KM HSOL 0.7934893 0.7943238 0.8186473

39 V KM DNIEB 0.6930369 0.7911324 0.819957

40 V KM DLAB 0.8039932 0.8184131 0.8227307

41 V KM COND 0.7926421 0.8253475 0.8419418

42 V KM CONALC 0.7024982 0.8332624 0.8472065

43 V KM RADAR 0.8029414 0.8421648 0.8328259

44 V KM SUSP 0.80169 0.8263395 0.8242046

45 V KM V EH10 0.7964532 0.8149253 0.8279104

46 V KM ABS 0.8025811 0.8026719 0.8147169

47 V KM LONRAC 0.8045783 0.7912803 0.8186206

48 V KM LONRED 0.7542224 0.7771379 0.8126447

49 V KM PPS 0.8024775 0.8077896 0.8164252

50 V KM PCR 0.7942209 0.8007252 0.8084237

51 V KM SDF 0.7018674 0.7161553 0.7477667

52 V KM SEMSAN 0.8015026 0.8028268 0.8129071

53 V KM DSCN 0.8596083 0.79339 0.804531

54 CONGAS PARO 0.810767 0.7143458 0.748188

55 CONGAS OCUP1 0.8019279 0.8333313 0.8387111

56 CONGAS OCUP4 0.7988748 0.8301117 0.8582663

57 CONGAS PRCRN 0.7953983 0.8191112 0.8424202

58 CONGAS IPI 0.8181123 0.8024005 0.8117343

59 CONGAS PCONCEM 0.8237281 0.7928198 0.8051074

60 CONGAS MANT 0.8292634 0.7248405 0.7485408

61 CONGAS PRECOML 0.8426114 0.8029551 0.8121599

62 CONGAS PREC 0.8214007 0.7933023 0.8119313

63 CONGAS HSOL 0.8081024 0.7169706 0.7549123

64 CONGAS DNIEB 0.8026749 0.8186196 0.8013039

65 CONGAS DLAB 0.7975095 0.8176019 0.7279907

66 CONGAS COND 0.7874491 0.7214555 0.6721187

67 CONGAS CONALC 0.8072548 0.8019044 0.8134041

68 CONGAS RADAR 0.7995603 0.79893 0.8072544

69 CONGAS SUSP 0.7117075 0.6943242 0.8002756

70 CONGAS V EH10 0.8021846 0.8018988 0.8131273

71 CONGAS ABS 0.7896054 0.7971026 0.8115512

72 CONGAS LONRAC 0.7057952 0.7761258 0.710728

73 CONGAS LONRED 0.8337116 0.803909 0.8135646

74 CONGAS PPS 0.8339543 0.8016799 0.6754979

75 CONGAS PCR 0.8260382 0.7972781 0.6657882

76 CONGAS SDF 0.8015085 0.8191803 0.8110915

77 CONGAS SEMSAN 0.7909441 0.810806 0.4786969

78 CONGAS DSCN 0.7084325 0.7536537 0.606624

79 PARO OCUP1 0.8027989 0.81485 0.8119726

80 PARO OCUP4 0.7900512 0.8204957 0.8041709

M X1 X2 λX = −0.5 λX = 0.1 λX = 0.5

81 PARO PRCRN 0.709393 0.8112935 0.799443

82 PARO IPI 0.817981 0.813485 0.8096414

83 PARO PCONCEM 0.8657481 0.8068974 0.815507

84 PARO MANT 0.8485372 0.7591413 0.8244092

85 PARO PRECOML 0.8193548 0.8039355 0.8326634

86 PARO PREC 0.8603456 0.7994843 0.8173454

87 PARO HSOL 0.8379193 0.7234451 0.8106285

88 PARO DNIEB 0.8171518 0.8015966 0.8121349

89 PARO DLAB 0.8593346 0.8016541 0.8045158

90 PARO COND 0.8590953 0.7954139 0.7919884

91 PARO CONALC 0.8186303 0.8033172 0.6662796

92 PARO RADAR 0.8599243 0.8059517 0.66751

93 PARO SUSP 0.845686 0.7687274 0.6691402

94 PARO V EH10 0.8167623 0.8032978 0.6653

95 PARO ABS 0.8619321 0.8023057 0.6654278

96 PARO LONRAC 0.862701 0.7337906 0.667138

97 PARO LONRED 0.8325585 0.8031045 0.8457149

98 PARO PPS 0.867736 0.8483223 0.8002327

99 PARO PCR 0.8496205 0.7554901 0.7671273

100 PARO SDF 0.8206047 0.8022563 0.6661761

101 PARO SEMSAN 0.8706911 0.7992259 0.6672496

102 PARO DSCN 0.8270232 0.7957522 0.668268

103 OCUP1 OCUP4 0.8181561 0.8183737 0.6669999

104 OCUP1 PRCRN 0.8604405 0.8230952 0.6683062

105 OCUP1 IPI 0.8477729 0.8262305 0.6694916

106 OCUP1 PCONCEM 0.8085033 0.8427564 0.8039146

107 OCUP1 MANT 0.8671118 0.83703 0.8020617

108 OCUP1 PRECOML 0.8447033 0.8090556 0.7960699

109 OCUP1 PREC 0.8252275 0.8027668 0.8039556

110 OCUP1 HSOL 0.8706435 0.7971233 0.8044677

111 OCUP1 DNIEB 0.8418557 0.7877588 0.7453765

112 OCUP1 DLAB 0.8116384 0.8077051 0.8043248

113 OCUP1 COND 0.8723929 0.8018738 0.7291518

114 OCUP1 CONALC 0.8375506 0.732387 0.6787788

115 OCUP1 RADAR 0.8190067 0.8034062 0.8010043

116 OCUP1 SUSP 0.8715686 0.7970314 0.5361637

117 OCUP1 V EH10 0.8507222 0.7261359 0.7308758

118 OCUP1 ABS 0.8151765 0.8342945 0.8013602

119 OCUP1 LONRAC 0.8702629 0.8348999 0.7998687

120 OCUP1 LONRED 0.8326637 0.8283952 0.7962436

121 OCUP1 PPS 0.816782 0.8025501 0.8165366

122 OCUP1 PCR 0.8584543 0.7968542 0.8191087

123 OCUP1 SDF 0.8545053 0.7361098 0.8229729

124 OCUP1 SEMSAN 0.8163241 0.8018586 0.842477

125 OCUP1 DSCN 0.8693568 0.7966464 0.8181047

126 OCUP4 PRCRN 0.8449012 0.7319608 0.8099033

127 OCUP4 IPI 0.8164593 0.8164723 0.8035007

128 OCUP4 PCONCEM 0.8748668 0.7091916 0.7992298

129 OCUP4 MANT 0.8370542 0.6231448 0.7863793

130 OCUP4 PRECOML 0.8231295 0.8159253 0.798784

M X1 X2 λX = −0.5 λX = 0.1 λX = 0.5

131 OCUP4 PREC 0.8712107 0.8076577 0.7358418

132 OCUP4 HSOL 0.8085898 0.7780075 0.6752643

133 OCUP4 DNIEB 0.818318 0.8053004 0.7920324

134 OCUP4 DLAB 0.8599455 0.806879 0.7248855

135 OCUP4 COND 0.8552877 0.7985435 0.673356

136 OCUP4 CONALC 0.8204952 0.784465 0.8377942

137 OCUP4 RADAR 0.8651884 0.5655491 0.8486993

138 OCUP4 SUSP 0.8799376 0.6208145 0.853941

139 OCUP4 V EH10 0.8383208 0.8267241 0.7920708

140 OCUP4 ABS 0.8556648 0.7446674 0.7364794

141 OCUP4 LONRAC 0.8589986 0.6961203 0.6674088

142 OCUP4 LONRED 0.8175199 0.7877541 0.7919534

143 OCUP4 PPS 0.8600844 0.5632836 0.7280612

144 OCUP4 PCR 0.8477131 0.6144382 0.6776355

145 OCUP4 SDF 0.8127813 0.7850196 0.8032572

146 OCUP4 SEMSAN 0.8713335 0.6786676 0.8058785

147 OCUP4 DSCN 0.838255 0.6575677 0.8004544

148 PRCRN IPI 0.809005 0.8174156 0.8026858

149 PRCRN PCONCEM 0.8718846 0.8185809 0.8071421

150 PRCRN MANT 0.8376584 0.812004 0.8007521

151 PRCRN PRECOML 0.8364227 0.8183428 0.8019024

152 PRCRN PREC 0.8774896 0.7966366 0.849601

153 PRCRN HSOL 0.8628281 0.6618719 0.8422259

154 PRCRN DNIEB 0.8090952 0.8179866 0.8021276

155 PRCRN DLAB 0.8752892 0.5316843 0.800468

156 PRCRN COND 0.8487674 0.6117747 0.7968869

157 PRCRN CONALC 0.808623 0.8123097 0.8184171

158 PRCRN RADAR 0.8720834 0.4364196 0.8241593

159 PRCRN SUSP 0.8403805 0.5993511 0.8293394

160 PRCRN V EH10 0.8026666 0.8113697 0.8425349

161 PRCRN ABS 0.7954464 0.8153706 0.8308879

162 PRCRN LONRAC 0.7285878 0.8113417 0.8097642

163 PRCRN LONRED 0.8028518 0.8144649 0.802761

164 PRCRN PPS 0.8007795 0.8062329 0.8030566

165 PRCRN PCR 0.7988766 0.8224995 0.7976037

166 PRCRN SDF 0.8023547 0.8500317 0.8072577

167 PRCRN SEMSAN 0.7884496 0.8362918 0.8047019

168 PRCRN DSCN 0.7339607 0.827002 0.7986949

169 IPI PCONCEM 0.8027135 0.8172644 0.8029824

170 IPI MANT 0.7944165 0.8138492 0.8012297

171 IPI PRECOML 0.76845 0.7995465 0.796285

172 IPI PREC 0.8189657 0.7787061 0.8341185

173 IPI HSOL 0.8352812 0.5610755 0.8323098

174 IPI DNIEB 0.814536 0.6193843 0.8284105

175 IPI DLAB 0.8019226 0.7473589 0.8022876

176 IPI COND 0.823622 0.5644437 0.8013616

177 IPI CONALC 0.814046 0.6205317 0.7966963

178 IPI RADAR 0.8026382 0.8304521 0.8026443

179 IPI SUSP 0.7974025 0.7906591 0.8016385

180 IPI V EH10 0.7819428 0.7464324 0.7958521

M X1 X2 λX = −0.5 λX = 0.1 λX = 0.5

181 IPI ABS 0.804043 0.7581114 0.8024189

182 IPI LONRAC 0.8040253 0.5585804 0.8067381

183 IPI LONRED 0.7992863 0.6167365 0.7187955

184 IPI PPS 0.8188207 0.7513783 0.803302

185 IPI PCR 0.8112056 0.5579529 0.7815464

186 IPI SDF 0.780273 0.6191529 0.6471709

187 IPI SEMSAN 0.8147661 0.8015906 0.8027459

188 IPI DSCN 0.8178912 0.7960677 0.805073

189 PCONCEM MANT 0.7958295 0.7726824 0.7988621

190 PCONCEM PRECOML 0.8125099 0.8034616 0.8184416

191 PCONCEM PREC 0.8018711 0.8002722 0.8278837

192 PCONCEM HSOL 0.7712741 0.8006085 0.8295076

193 PCONCEM DNIEB 0.8037809 0.8159733 0.8426265

194 PCONCEM DLAB 0.8029221 0.59225 0.8084854

195 PCONCEM COND 0.7664897 0.6201463 0.8074731

196 PCONCEM CONALC 0.8027254 0.8157316 0.8020523

197 PCONCEM RADAR 0.7999521 0.7132975 0.806531

198 PCONCEM SUSP 0.7961661 0.6932914 0.7912557

199 PCONCEM V EH10 0.8025988 0.811743 0.8076371

200 PCONCEM ABS 0.8084887 0.5918014 0.8113267

201 PCONCEM LONRAC 0.780903 0.6081571 0.719124

202 PCONCEM LONRED 0.8022382 0.8030331 0.8031865

203 PCONCEM PPS 0.802995 0.6575 0.809543

204 PCONCEM PCR 0.777027 0.6777468 0.7183791

205 PCONCEM SDF 0.8024647 0.8022493 0.8337897

206 PCONCEM SEMSAN 0.8571991 0.8088987 0.8314761

207 PCONCEM DSCN 0.8300805 0.8034591 0.7791769

208 MANT PRECOML 0.8025315 0.8029373 0.8031629

209 MANT PREC 0.799095 0.7964026 0.8088327

210 MANT HSOL 0.7945355 0.6804436 0.71785

211 MANT DNIEB 0.8185302 0.8018515 0.8027029

212 MANT DLAB 0.8262494 0.6325564 0.8085434

213 MANT COND 0.8341029 0.6247462 0.718098

214 MANT CONALC 0.8421848 0.801266 0.8018244

215 MANT RADAR 0.8195827 0.5295981 0.4570613

216 MANT SUSP 0.8037528 0.6330832 0.6117017

217 MANT V EH10 0.8020468 0.8013577 0.802367

218 MANT ABS 0.7983169 0.8046625 0.8062233

219 MANT LONRAC 0.7892269 0.8022003 0.8021456

220 MANT LONRED 0.8072559 0.8182096 0.8185569

221 MANT PPS 0.803381 0.8252102 0.818127

222 MANT PCR 0.776737 0.8326215 0.8217059

223 MANT SDF 0.804149 0.8427287 0.8427956

224 MANT SEMSAN 0.7993248 0.8249284 0.8255273

225 MANT DSCN 0.7739915 0.8172542 0.8128662

226 PRECOML PREC 0.8335713 0.8018802 0.8026256

227 PRECOML HSOL 0.840189 0.8034711 0.8042399

228 PRECOML DNIEB 0.8430549 0.7925271 0.7940023

229 PRECOML DLAB 0.80299 0.8067066 0.8081479

230 PRECOML COND 0.8007227 0.6220574 0.6832529

M X1 X2 λX = −0.5 λX = 0.1 λX = 0.5

231 PRECOML CONALC 0.7748959 0.6271633 0.6755643

232 PRECOML RADAR 0.8027776 0.8020155 0.8038543

233 PRECOML SUSP 0.7995724 0.6342282 0.6826434

234 PRECOML V EH10 0.7766107 0.6326462 0.6751984

235 PRECOML ABS 0.802318 0.8336061 0.8343619

236 PRECOML LONRAC 0.8342743 0.8325257 0.8098646

237 PRECOML LONRED 0.8271725 0.8175785 0.7711921

238 PRECOML PPS 0.8018639 0.8020362 0.802144

239 PRECOML PCR 0.7950026 0.5869677 0.6901301

240 PRECOML SDF 0.3463804 0.6217626 0.6757403

241 PRECOML SEMSAN 0.8024319 0.8010321 0.8026746

242 PRECOML DSCN 0.8017316 0.5982199 0.6853769

243 PREC HSOL 0.6089112 0.6226696 0.6752623

244 PREC DNIEB 0.8141246 0.8041385 0.8010191

245 PREC DLAB 0.7789798 0.8015598 0.8482312

246 PREC COND 0.389691 0.7961804 0.8460647

247 PREC CONALC 0.8021586 0.8173462 0.8178381

248 PREC RADAR 0.7655609 0.8067594 0.8137785

249 PREC SUSP 0.3868807 0.7852026 0.8421694

250 PREC V EH10 0.8016922 0.8154004 0.8435518

251 PREC ABS 0.8003895 0.816497 0.8700421

252 PREC LONRAC 0.7648491 0.80605 0.8599413

253 PREC LONRED 0.804109 0.812376 0.8023709

254 PREC PPS 0.7983945 0.7997876 0.8454726

255 PREC PCR 0.7808899 0.7807682 0.8352669

256 PREC SDF 0.8171735 0.8022594 0.8061961

257 PREC SEMSAN 0.7970394 0.7947252 0.4387541

258 PREC DSCN 0.6428801 0.7753979 0.6134612

259 HSOL DNIEB 0.814799 0.8028456 0.8015362

260 HSOL DLAB 0.813954 0.8097876 0.4400104

261 HSOL COND 0.7865152 0.8014919 0.6121818

262 HSOL CONALC 0.8119278 0.8030266 0.8331818

263 HSOL RADAR 0.7908942 0.8043954 0.7621032

264 HSOL SUSP 0.6154104 0.7859217 0.7168892

265 HSOL V EH10 0.8031204 0.8025347 0.8005233

266 HSOL ABS 0.7781173 0.7985959 0.417049

267 HSOL LONRAC 0.5328157 0.7771499 0.6044848

268 HSOL LONRED 0.8025323 0.8022483 0.8007875

269 HSOL PPS 0.8220255 0.8393333 0.4426737

270 HSOL PCR 0.8097165 0.823342 0.6105403

271 HSOL SDF 0.8033353 0.8011687 0.818186

272 HSOL SEMSAN 0.795472 0.8022975 0.8233175

273 HSOL DSCN 0.6633954 0.8044716 0.8283526

274 DNIEB DLAB 0.802295 0.8180137 0.8426477

275 DNIEB COND 0.7840268 0.8217409 0.839265

276 DNIEB CONALC 0.6002579 0.8252991 0.8248309

277 DNIEB RADAR 0.8011525 0.8430021 0.8020027

278 DNIEB SUSP 0.8166035 0.8470611 0.7983913

279 DNIEB V EH10 0.6704432 0.845627 0.8011711

280 DNIEB ABS 0.8013855 0.8025935 0.8054063

M X1 X2 λX = −0.5 λX = 0.1 λX = 0.5

281 DNIEB LONRAC 0.8328708 0.8005556 0.8019902

282 DNIEB LONRED 0.8408698 0.7884685 0.7980442

283 DNIEB PPS 0.8178589 0.8066005 0.802572

284 DNIEB PCR 0.8203434 0.7973721 0.7984923

285 DNIEB SDF 0.8095639 0.7767379 0.7960865

286 DNIEB SEMSAN 0.8437495 0.8034665 0.833557

287 DNIEB DSCN 0.8535188 0.7935704 0.8315013

288 DLAB COND 0.8443313 0.7700073 0.8285805

289 DLAB CONALC 0.8023017 0.83411 0.8012303

290 DLAB RADAR 0.8205853 0.831187 0.7985719

291 DLAB SUSP 0.8076937 0.8203379 0.7950395

292 DLAB V EH10 0.8064329 0.801958 0.8012164

293 DLAB ABS 0.7825408 0.7943072 0.7991429

294 DLAB LONRAC 0.5154273 0.7742683 0.7954598

295 DLAB LONRED 0.8018405 0.8012321 0.826621

296 DLAB PPS 0.7773717 0.7955405 0.8264926

297 DLAB PCR 0.4799133 0.7742258 0.8299019

298 DLAB SDF 0.8332608 0.8155321 0.8184026

299 DLAB SEMSAN 0.8202554 0.8096874 0.8230121

300 DLAB DSCN 0.6480552 0.7997965 0.8279362

301 COND CONALC 0.8019845 0.8122241 0.7970354

302 COND RADAR 0.7802844 0.8163128 0.8134748

303 COND SUSP 0.5371699 0.8075223 0.820856

304 COND V EH10 0.8017459 0.8096658 0.79607

305 COND ABS 0.7795558 0.8025701 0.8120152

306 COND LONRAC 0.5022017 0.7949075 0.8201797

307 COND LONRED 0.8020302 0.8044701 0.8436118

308 COND PPS 0.8088196 0.8008472 0.8480323

309 COND PCR 0.812897 0.7961977 0.8515208

310 COND SDF 0.8026744 0.8038579 0.7983258

311 COND SEMSAN 0.8014651 0.8040571 0.8107866

312 COND DSCN 0.7993778 0.8020434 0.8209671

313 CONALC RADAR 0.8183627 0.804085 0.7939811

314 CONALC SUSP 0.8228468 0.8120772 0.8109269

315 CONALC V EH10 0.8227236 0.8023296 0.8209948

316 CONALC ABS 0.8023917 0.8040464 0.8427443

317 CONALC LONRAC 0.8120209 0.8091219 0.8421057

318 CONALC LONRED 0.81337 0.805031 0.8377355

319 CONALC PPS 0.8028692 0.803712 0.8332441

320 CONALC PCR 0.8354772 0.8137141 0.8220741

321 CONALC SDF 0.8148162 0.8297172 0.8149056

322 CONALC SEMSAN 0.8044048 0.8039758 0.8335598

323 CONALC DSCN 0.8040421 0.8030754 0.816103

324 RADAR SUSP 0.8027946 0.800414 0.809433

325 RADAR V EH10 0.8187281 0.8192675 0.8347794

326 RADAR ABS 0.8150761 0.8238789 0.8373343

327 RADAR LONRAC 0.8096017 0.8284216 0.8355959

328 RADAR LONRED 0.8142254 0.8374016 0.821199

329 RADAR PPS 0.8199405 0.8104663 0.8110525

330 RADAR PCR 0.8218945 0.8067558 0.806878

M X1 X2 λX = −0.5 λX = 0.1 λX = 0.5

331 RADAR SDF 0.8133328 0.8043737 0.8211055

332 RADAR SEMSAN 0.8080674 0.8027013 0.8113551

333 RADAR DSCN 0.8034381 0.7983248 0.8069341

334 SUSP V EH10 0.8036057 0.8097748 0.8073548

335 SUSP ABS 0.8039292 0.8082205 0.8013315

336 SUSP LONRAC 0.8008538 0.8029621 0.7909047

337 SUSP LONRED 0.8029065 0.8048129 0.8028127

338 SUSP PPS 0.8015424 0.8034583 0.7978693

339 SUSP PCR 0.7984759 0.7980875 0.7876263

340 SUSP SDF 0.8024696 0.8361496 0.8336978

341 SUSP SEMSAN 0.8080495 0.8376428 0.831532

342 SUSP DSCN 0.8034414 0.8366434 0.8234911

343 V EH10 ABS 0.8024877 0.8041964 0.8020142

344 V EH10 LONRAC 0.8092256 0.8029364 0.798101

345 V EH10 LONRED 0.8032036 0.797426 0.7882843

346 V EH10 PPS 0.8027529 0.8036126 0.8017914

347 V EH10 PCR 0.855589 0.8019825 0.7985028

348 V EH10 SDF 0.8530131 0.7978273 0.7876679

349 V EH10 SEMSAN 0.8024791 0.8221404 0.6769551

350 V EH10 DSCN 0.8067071 0.8018141 0.6769551

351 ABS LONRAC 0.8007792 0.7589147 0.6769551

352 ABS LONRED 0.8185386 0.6185572 0.8375151

353 ABS PPS 0.8243669 0.6565701 0.8020374

354 ABS PCR 0.8310752 0.6659081 0.772318

355 ABS SDF 0.8426902 0.8003165 0.6771796

356 ABS SEMSAN 0.8366697 0.7331786 0.6771796

357 ABS DSCN 0.8103501 0.6737012 0.6771796

358 LONRAC LONRED 0.8022304 0.8180917 0.6773342

359 LONRAC PPS 0.8303597 0.813956 0.6773342

360 LONRAC PCR 0.815368 0.8059941 0.6773342

361 LONRAC SDF 0.807937 0.818143 0.8370532

362 LONRAC SEMSAN 0.8064075 0.8133426 0.8013598

363 LONRAC DSCN 0.801271 0.714338 0.7711194

364 LONRED PPS 0.8038055 0.8187184 0.6770562

365 LONRED PCR 0.8022871 0.6769864 0.6770562

366 LONRED SDF 0.7992827 0.6711104 0.6770562

367 LONRED SEMSAN 0.8339847 0.8156877 0.6770441

368 LONRED DSCN 0.8329483 0.4582689 0.6770441

369 PPS PCR 0.8318461 0.6119364 0.6770441

370 PPS SDF 0.8035692 0.8163935 0.8445552

371 PPS SEMSAN 0.8019062 0.8118677 0.8230756

372 PPS DSCN 0.7988585 0.806015 0.7910318

373 PCR SDF 0.8027218 0.7893519 0.8364614

374 PCR SEMSAN 0.8020762 0.8113378 0.8031359

375 PCR DSCN 0.8000596 0.8223714 0.7722329

376 SDF SEMSAN 0.8028954 0.8495689 0.6770119

377 SDF DSCN 0.7964628 0.8251071 0.6770119

378 SEMSAN DSCN 0.7370984 0.8171374 0.6770119

Appendix V: SE Bayesian Estimation: Model

Selection

M DIC β1 β2 β3 β4 β5 β6 β7 β8 β9 β10 β11

1 93 -115.708 -25.241 17.424 -368.619 57.754 6.029 -79.059 169.543 98.314 2.833 -0.206

2 100 5.409 -0.070 -59.985 -806.879 -38.496 -3.222 -34.261 461.951 212.396 4.460 -0.132

3 87 0.056 0.102 -11.121 -663.105 26.163 2.215 21.618 309.252 133.747 2.847 -0.201

4 88 -82.098 -67.031 4.820 -561.965 30.528 2.394 7.157 259.959 127.351 2.833 -0.132

5 90 6.121 5.192 -13.603 -447.450 73.678 4.463 1.839 236.600 110.671 1.839 -0.405

6 86 0.064 0.087 -1.637 -582.138 51.217 3.739 -8.615 278.786 118.514 2.536 -0.258

7 90 -95.596 -42.909 0.553 -558.288 7.587 3.106 -43.645 272.609 129.515 3.725 -0.010

8 104 6.387 0.563 -1.445 -405.467 85.757 2.509 -26.578 271.031 146.527 1.140 -0.682

9 86 0.060 0.098 -0.228 -575.527 57.614 3.457 7.211 282.380 115.225 2.213 -0.315

10 87 -68.120 -83.532 -4.300 11.667 -8.176 -5.756 33.468 194.936 141.601 2.181 -0.145

11 91 6.816 3.334 15.861 6.846 -13.131 -9.111 -6.384 357.494 113.671 1.638 -0.285

12 86 0.061 0.090 3.754 10.540 -10.695 -7.680 13.054 309.545 128.581 1.994 -0.231

13 87 -69.234 -81.049 -1.442 11.694 -7.704 -5.246 31.384 167.352 141.428 2.109 -0.200

14 88 5.710 5.829 -10.300 9.380 -9.915 -8.050 7.876 221.839 123.017 1.801 -0.313

15 86 0.057 0.101 -4.701 11.596 -8.846 -7.297 16.807 231.506 130.142 2.098 -0.252

16 87 -68.076 -82.125 0.011 11.582 -8.279 -5.777 27.188 192.572 142.101 2.091 -0.183

17 91 6.370 4.463 -0.544 7.605 -11.843 -8.836 1.825 286.360 116.388 1.603 -0.321

18 86 0.061 0.091 -0.200 10.710 -9.992 -7.661 12.981 288.326 125.172 1.999 -0.262

19 85 -55.114 -86.257 -29.657 0.066 -0.037 -0.260 29.781 152.211 173.093 3.372 -0.017

20 105 8.206 -4.477 0.121 0.024 -0.225 -0.758 -19.783 577.875 163.574 1.800 -0.347

21 86 0.054 0.110 -4.265 0.042 -0.157 -0.518 59.067 396.768 139.463 1.698 -0.233

22 86 -59.162 -89.265 2.114 0.052 -0.079 -0.410 39.753 149.978 151.222 2.341 -0.182

23 90 5.492 6.016 -13.001 0.039 -0.122 -0.648 18.470 193.459 125.818 1.745 -0.365

24 85 0.054 0.110 -3.424 0.049 -0.099 -0.583 20.651 207.209 132.282 2.248 -0.271

25 85 -57.897 -92.016 0.313 0.056 -0.080 -0.368 45.238 167.039 157.219 2.486 -0.131

26 96 6.869 2.203 -1.073 0.021 -0.188 -0.814 -3.375 315.853 116.848 0.999 -0.493

27 86 0.055 0.106 -0.271 0.043 -0.127 -0.600 41.440 260.030 133.581 1.818 -0.308

28 97 -118.214 -23.467 19.181 -312.421 61.388 5.824 0.649 -0.115 -1.009 3.068 -0.213

29 90 5.405 4.506 -23.480 -544.419 43.846 0.153 -0.279 -0.369 -3.320 2.528 -0.161

30 90 0.069 0.074 4.478 -455.090 63.819 4.187 0.297 -0.208 -1.553 2.675 -0.213

187


31 91 -82.733 -60.597 11.108 -509.968 40.290 1.048 -0.045 -0.283 -2.561 2.780 -0.085

32 91 5.972 5.121 -6.802 -421.800 80.403 2.910 -0.080 -0.240 -2.471 1.747 -0.349

33 89 0.062 0.085 4.773 -516.963 59.205 2.125 -0.030 -0.303 -2.387 2.413 -0.208

34 96 -106.780 -25.636 0.871 -449.762 15.498 2.310 0.517 -0.309 -1.711 4.244 0.084

35 93 5.672 3.468 -0.076 -483.558 78.851 1.001 -0.354 -0.330 -3.407 1.602 -0.375

36 89 0.065 0.076 0.484 -497.092 42.124 2.407 0.180 -0.311 -1.997 3.085 -0.094

37 88 -60.058 -82.295 -21.493 13.231 -6.221 -2.609 -0.146 -0.173 -3.158 2.585 -0.061

38 90 5.811 4.404 -7.732 8.519 -11.193 -4.485 -0.157 -0.344 -2.925 1.853 -0.180

39 87 0.054 0.097 -16.912 11.875 -8.504 -3.926 -0.124 -0.263 -2.916 2.386 -0.123

40 88 -68.102 -78.047 3.410 11.646 -7.000 -4.358 -0.121 -0.138 -2.918 2.243 -0.159

41 90 5.550 5.563 -4.335 9.117 -10.033 -6.012 -0.061 -0.216 -2.646 1.786 -0.273

42 87 0.055 0.102 0.731 11.015 -8.590 -5.319 -0.061 -0.197 -2.648 2.131 -0.218

43 88 -63.315 -80.659 0.384 12.164 -6.888 -3.457 -0.160 -0.176 -3.016 2.338 -0.110

44 90 5.801 4.744 -0.025 8.314 -11.288 -5.427 -0.122 -0.290 -2.787 1.712 -0.231

45 87 0.055 0.099 0.242 10.948 -8.806 -4.534 -0.117 -0.252 -2.815 2.167 -0.169

46 91 -62.472 -66.865 -38.643 0.079 0.027 -0.270 0.306 0.013 -2.982 4.823 0.079

47 90 4.957 4.258 -32.502 0.049 -0.114 -0.101 -0.395 -0.386 -3.966 2.400 -0.094

48 86 0.043 0.119 -34.439 0.068 -0.031 -0.273 0.027 -0.144 -3.177 3.681 -0.015

49 88 -59.449 -85.442 8.187 0.054 -0.065 -0.300 -0.182 -0.105 -3.147 2.588 -0.125

50 90 5.248 5.954 -6.387 0.039 -0.121 -0.499 -0.087 -0.182 -2.769 1.791 -0.316

51 87 0.050 0.112 2.584 0.050 -0.090 -0.418 -0.083 -0.164 -2.879 2.356 -0.216

52 87 -56.293 -80.994 0.977 0.065 -0.037 -0.197 -0.106 -0.143 -3.385 3.451 0.024

53 92 5.724 3.710 -0.067 0.034 -0.152 -0.373 -0.289 -0.326 -3.403 1.463 -0.317

54 86 0.047 0.114 0.519 0.054 -0.084 -0.309 -0.172 -0.221 -3.187 2.587 -0.136

55 97 -120.645 -18.407 19.761 -312.102 64.572 6.261 0.001 0.000 -0.007 2.875 -0.228

56 97 5.259 2.190 -47.466 -606.423 28.779 -2.881 0.000 0.000 -0.018 3.095 -0.106

57 90 0.063 0.087 -3.396 -481.118 55.281 3.168 0.000 0.000 -0.010 2.538 -0.200

58 91 -79.274 -69.005 7.276 -477.877 46.989 1.389 0.000 0.000 -0.012 2.468 -0.130

59 92 5.885 5.419 -11.624 -417.062 82.947 3.763 0.000 0.000 -0.011 1.684 -0.390

60 90 0.060 0.097 0.555 -483.024 58.327 2.689 0.000 0.000 -0.011 2.234 -0.258

61 93 -98.746 -36.730 0.859 -475.595 18.431 1.883 0.000 0.000 -0.011 3.739 0.062

62 103 6.210 0.942 -0.952 -373.656 95.433 1.894 0.000 0.000 -0.015 1.059 -0.636

63 89 0.058 0.099 0.182 -519.722 55.979 2.180 0.000 0.000 -0.012 2.323 -0.219

64 89 -66.042 -80.309 -12.939 11.124 -6.961 -3.458 0.000 0.000 -0.013 2.353 -0.105

65 93 6.137 4.124 -0.949 6.603 -12.468 -5.371 0.000 0.000 -0.012 1.708 -0.195

66 88 0.055 0.100 -8.997 9.938 -9.399 -4.791 0.000 0.000 -0.012 2.147 -0.152

67 90 -66.944 -80.837 0.566 10.957 -7.033 -4.841 0.000 0.000 -0.013 2.168 -0.179

68 91 5.493 6.021 -8.039 8.733 -10.054 -6.682 0.000 0.000 -0.011 1.752 -0.301

69 89 0.055 0.102 -2.435 10.783 -8.643 -6.221 0.000 0.000 -0.012 2.112 -0.250

70 89 -66.737 -80.612 0.220 10.691 -7.441 -4.030 0.000 0.000 -0.013 2.179 -0.148

71 92 5.976 4.742 -0.235 6.840 -11.877 -6.195 0.000 0.000 -0.011 1.599 -0.264

72 89 0.056 0.100 0.036 9.805 -9.467 -5.454 0.000 0.000 -0.012 2.021 -0.202

73 89 -58.241 -78.622 -31.289 0.069 -0.005 -0.294 0.000 0.000 -0.015 3.942 0.024

74 99 6.404 0.178 -22.704 0.026 -0.189 -0.145 0.000 0.000 -0.017 1.787 -0.162

75 88 0.046 0.115 -25.326 0.050 -0.089 -0.259 0.000 0.000 -0.015 2.600 -0.099

76 90 -60.878 -86.720 3.771 0.050 -0.067 -0.364 0.000 0.000 -0.013 2.500 -0.151

77 92 5.293 6.096 -11.263 0.037 -0.116 -0.621 0.000 0.000 -0.012 1.837 -0.352

78 88 0.050 0.117 -1.967 0.048 -0.087 -0.540 0.000 0.000 -0.012 2.342 -0.263

79 88 -54.659 -91.084 0.557 0.056 -0.060 -0.266 0.000 0.000 -0.015 2.746 -0.073

80 97 6.411 2.701 -0.674 0.020 -0.187 -0.585 0.000 0.000 -0.013 0.988 -0.420


81 88 0.157 0.245 0.005 0.497 -0.276 -0.105 -0.005 -0.010 -0.129 0.636 -0.011

82 97 -0.158 -0.340 0.555 -0.207 0.463 0.120 0.022 0.023 0.084 0.472 -0.025

83 90 0.884 1.432 0.294 -0.259 0.290 0.111 0.012 0.021 0.080 -1.840 -0.017

84 93 0.184 0.265 0.510 -0.236 0.417 0.139 0.016 0.025 0.076 -0.362 -0.025

85 103 -0.079 -0.449 1.934 -0.290 0.348 -0.017 0.041 0.037 0.134 -0.632 -0.013

86 90 0.659 1.869 0.630 -0.328 0.241 0.038 0.024 0.029 0.101 -2.242 -0.011

87 99 0.116 0.363 1.469 -0.311 0.329 0.016 0.038 0.041 0.123 -1.153 -0.014

88 100 -0.139 -0.384 -0.545 -0.202 0.543 0.108 0.031 0.026 0.093 1.506 -0.027

89 90 0.805 1.627 -0.250 -0.272 0.317 0.099 0.017 0.023 0.085 -1.425 -0.017

90 96 0.163 0.307 -0.494 -0.222 0.477 0.121 0.026 0.030 0.084 0.546 -0.026

91 94 -0.019 -0.498 -0.170 4.397 -0.833 0.269 0.037 0.013 0.162 -2.339 -0.013

92 86 0.456 1.861 -0.255 3.612 -0.610 -0.092 0.017 0.012 0.131 -4.121 -0.006

93 90 0.063 0.406 -0.151 4.208 -0.746 0.073 0.031 0.016 0.146 -3.027 -0.013

94 88 -0.077 -0.375 2.892 4.050 -0.266 0.073 0.014 0.013 0.149 -5.469 0.002

95 85 0.694 1.304 1.746 3.343 -0.421 -0.284 0.005 0.014 0.126 -5.519 -0.001

96 86 0.109 0.292 2.689 3.905 -0.198 -0.053 0.010 0.016 0.140 -5.904 0.001

97 91 -0.011 -0.492 0.554 4.831 -0.363 0.353 0.034 0.014 0.174 -4.084 -0.004

98 85 0.503 1.726 0.401 3.757 -0.414 -0.117 0.013 0.014 0.135 -5.012 -0.002

99 89 0.060 0.388 0.502 4.687 -0.256 0.203 0.028 0.017 0.156 -4.775 -0.005

100 98 -0.072 -0.477 0.404 0.474 -0.461 -0.070 0.039 0.021 0.121 1.054 -0.024

101 88 0.493 2.025 0.043 0.563 -0.279 -0.059 0.026 0.018 0.114 -1.925 -0.013

102 94 0.106 0.394 0.359 0.497 -0.404 -0.089 0.034 0.023 0.110 0.003 -0.023

103 94 0.000 -0.527 4.250 0.941 -0.145 0.077 0.040 0.024 0.178 -3.828 0.000

104 86 0.420 1.904 2.648 0.775 -0.102 -0.002 0.018 0.018 0.141 -4.810 -0.001

105 90 0.053 0.411 3.926 0.909 -0.125 0.052 0.037 0.028 0.165 -4.446 -0.001

106 99 -0.016 -0.569 -0.133 0.613 -0.464 -0.002 0.053 0.026 0.147 1.379 -0.022

107 88 0.375 2.235 0.121 0.641 -0.253 -0.035 0.029 0.018 0.125 -2.239 -0.010

108 96 0.067 0.462 -0.145 0.600 -0.418 -0.029 0.046 0.027 0.129 0.293 -0.021

109 101 -0.161 -0.328 0.532 -0.133 0.548 0.088 -0.114 -0.115 -0.437 1.148 -0.025

110 93 0.841 1.474 0.236 -0.207 0.366 0.075 -0.072 -0.105 -0.468 -1.120 -0.016

111 97 0.174 0.274 0.431 -0.168 0.506 0.096 -0.078 -0.128 -0.416 0.337 -0.023

112 105 -0.100 -0.389 2.598 -0.193 0.474 -0.101 -0.220 -0.245 -0.663 -0.144 -0.008

113 93 0.685 1.689 1.450 -0.258 0.312 -0.024 -0.124 -0.166 -0.560 -1.991 -0.007

114 105 -0.127 -0.387 -0.393 -0.123 0.634 0.032 -0.167 -0.157 -0.488 2.208 -0.025

115 94 0.774 1.640 -0.146 -0.204 0.394 0.042 -0.107 -0.126 -0.465 -0.781 -0.015

116 101 0.160 0.296 -0.328 -0.147 0.593 0.051 -0.124 -0.169 -0.450 1.147 -0.023

117 103 0.005 -0.532 -0.050 5.037 -0.781 0.387 -0.180 -0.026 -0.852 -1.987 -0.016

118 90 0.313 2.211 -0.208 3.531 -0.740 0.028 -0.108 -0.036 -0.731 -3.249 -0.008

119 99 0.034 0.459 -0.081 4.542 -0.693 0.315 -0.139 -0.047 -0.768 -2.603 -0.016

120 92 -0.055 -0.399 3.629 4.133 -0.212 0.325 -0.098 -0.058 -0.885 -5.380 0.003

121 88 0.591 1.470 2.241 3.301 -0.459 -0.085 -0.041 -0.058 -0.737 -5.221 0.000

122 88 3.374 9.198 18.425 14.610 -2.777 -0.816 -0.139 -0.155 -3.353 -80.647 -0.005

123 89 0.028 0.157 27.304 17.531 -1.196 1.777 -0.195 -0.204 -3.689 -88.545 0.042

124 100 14.445 -158.187 1.146 23.291 -2.383 6.716 -0.678 -0.134 -4.434 -52.406 -0.172

125 89 1.957 12.862 0.879 16.500 -2.844 1.098 -0.357 -0.147 -3.547 -66.103 -0.075

126 96 0.006 0.230 1.062 21.622 -1.989 5.010 -0.542 -0.186 -3.962 -61.819 -0.168

127 105 -35.472 -131.421 37.418 0.026 -0.229 -0.168 -0.612 -0.288 -2.571 33.998 -0.628

128 92 2.831 13.070 9.366 0.038 -0.148 -0.220 -0.406 -0.202 -2.628 -14.740 -0.351

129 100 0.033 0.195 30.720 0.031 -0.213 -0.223 -0.503 -0.315 -2.344 16.865 -0.561

130 100 -1.665 -144.610 40.987 0.069 -0.102 0.649 -0.806 -0.433 -4.280 -43.614 0.017


131 90 2.045 12.840 25.021 0.059 -0.065 0.170 -0.408 -0.261 -3.473 -62.270 0.007

132 97 0.015 0.205 38.269 0.067 -0.091 0.531 -0.656 -0.459 -3.901 -55.147 0.018

133 104 -9.943 -159.736 -0.371 0.037 -0.247 0.192 -0.900 -0.398 -3.096 46.936 -0.537

134 92 1.841 15.080 0.218 0.045 -0.138 0.010 -0.526 -0.248 -2.955 -17.268 -0.271

135 103 0.021 0.228 -0.372 0.035 -0.231 0.091 -0.773 -0.431 -2.706 27.826 -0.505

136 100 -64.283 -98.718 30.280 -239.381 164.063 2.472 -0.001 0.000 -0.011 13.009 -0.525

137 92 4.676 9.242 11.987 -355.710 111.849 2.234 0.000 0.000 -0.011 -22.975 -0.348

138 97 0.051 0.140 25.887 -292.537 151.536 2.845 0.000 0.000 -0.011 0.038 -0.501

139 101 -43.910 -110.440 18.766 -335.381 135.326 -2.715 -0.001 0.000 -0.016 -10.058 -0.143

140 92 4.001 10.100 10.562 -405.515 85.025 -0.181 -0.001 0.000 -0.013 -37.221 -0.164

141 98 0.041 0.152 18.254 -363.593 123.636 -1.902 -0.001 0.000 -0.015 -23.458 -0.153

142 103 -54.229 -110.129 -0.512 -220.706 185.320 0.779 -0.001 0.000 -0.013 23.983 -0.493

143 93 4.278 10.281 -0.136 -355.745 112.006 1.478 -0.001 0.000 -0.012 -20.209 -0.320

144 99 0.047 0.151 -0.467 -253.765 169.958 1.475 -0.001 0.000 -0.012 8.968 -0.483

145 100 0.952 -152.575 -6.427 18.641 -4.520 2.722 -0.001 0.000 -0.019 -28.823 -0.362

146 91 2.162 12.762 -15.399 14.744 -3.814 -0.463 0.000 0.000 -0.016 -56.701 -0.159

147 96 0.011 0.225 -8.515 17.941 -3.600 1.725 -0.001 0.000 -0.017 -43.143 -0.322

148 92 -28.220 -111.875 25.520 16.591 -1.516 1.854 0.000 0.000 -0.018 -79.164 0.047

149 88 3.541 9.230 15.312 13.643 -2.650 -1.939 0.000 0.000 -0.015 -80.962 -0.008

150 89 0.094 0.323 2.870 3.653 -0.198 0.042 -0.011 -0.008 -0.165 -5.598 0.001

151 98 0.013 -0.544 0.553 4.497 -0.355 0.516 -0.040 -0.005 -0.206 -3.421 -0.006

152 90 0.416 1.912 0.414 3.459 -0.378 0.009 -0.015 -0.006 -0.159 -4.648 -0.002

153 94 0.034 0.448 0.503 4.354 -0.293 0.336 -0.029 -0.007 -0.186 -4.151 -0.005

154 102 -0.068 -0.484 0.377 0.327 -0.487 -0.038 -0.043 -0.013 -0.148 1.604 -0.024

155 92 0.461 2.106 0.042 0.463 -0.295 -0.043 -0.026 -0.009 -0.138 -1.546 -0.013

156 99 0.098 0.402 0.326 0.386 -0.445 -0.049 -0.032 -0.014 -0.135 0.489 -0.022

157 97 -0.020 -0.489 4.254 0.708 -0.212 0.111 -0.047 -0.019 -0.205 -3.077 0.001

158 90 0.422 1.905 2.638 0.644 -0.137 0.009 -0.021 -0.011 -0.164 -4.281 0.000

159 95 0.057 0.400 4.028 0.699 -0.179 0.091 -0.035 -0.022 -0.185 -3.851 0.001

160 103 -0.021 -0.564 -0.042 0.401 -0.514 0.049 -0.061 -0.020 -0.174 1.971 -0.019

161 92 0.341 2.307 0.174 0.527 -0.260 -0.005 -0.030 -0.011 -0.152 -1.876 -0.010

162 99 0.061 0.464 -0.005 0.431 -0.456 0.028 -0.049 -0.021 -0.160 0.731 -0.018

163 101 -93.952 -62.678 54.961 -195.217 165.091 6.263 65.870 272.379 96.467 1.597 -0.591

164 87 5.427 6.473 -3.838 -424.376 28.994 2.381 -11.284 242.350 130.135 -41.724 -0.143

165 92 0.063 0.110 33.684 -321.038 118.653 5.328 48.194 276.551 98.966 -13.008 -0.454

166 90 -69.226 -72.728 22.819 -503.951 -2.989 -0.093 27.816 322.431 163.093 -53.042 0.095

167 87 5.651 5.899 -0.333 -427.796 34.125 2.765 -14.179 235.058 127.130 -40.875 -0.167

168 86 0.054 0.104 15.411 -531.713 10.167 1.264 2.256 320.391 146.315 -50.507 -0.002

169 126 -59.114 -73.408 2.815 -27.819 81.631 3.391 82.620 343.908 175.479 -24.558 -0.094

170 87 5.462 6.069 0.221 -435.914 20.746 2.194 -11.900 238.974 132.530 -45.072 -0.111

171 102 0.052 0.155 -0.219 -267.150 169.543 4.608 176.198 534.729 126.685 0.574 -0.396

172 87 -45.547 -95.200 -25.406 13.793 -2.345 -0.806 50.789 142.125 185.570 -45.151 -0.016

173 88 5.774 4.507 -9.127 8.510 -6.287 -5.958 -32.644 255.969 143.462 -44.209 -0.058

174 85 0.047 0.116 -18.823 12.091 -3.617 -3.491 18.869 206.585 163.380 -46.321 -0.047

175 87 -59.865 -85.596 6.377 11.149 -4.744 -3.227 36.127 155.422 160.737 -38.963 -0.077

176 87 5.316 6.097 -3.408 8.795 -7.161 -5.931 -7.708 206.177 135.022 -35.142 -0.183

177 86 0.052 0.107 2.731 10.745 -5.305 -4.785 7.757 211.701 147.996 -39.911 -0.139

178 86 -53.927 -88.050 0.565 12.299 -3.603 -2.109 38.561 179.412 171.139 -43.352 -0.024

179 87 5.765 4.966 -0.037 7.979 -7.060 -6.352 -33.451 238.497 133.311 -38.753 -0.137

180 85 0.050 0.109 0.347 11.299 -4.972 -4.424 3.717 217.470 153.335 -43.039 -0.091


181 113 -38.232 -84.029 40.850 0.124 -0.007 0.027 59.829 189.670 201.728 -33.259 -0.314

182 87 4.063 7.372 -25.966 0.052 -0.026 -0.204 14.996 184.969 174.461 -52.039 0.010

183 94 0.026 0.203 19.049 0.059 -0.095 -0.221 187.094 192.628 168.123 -13.321 -0.465

184 86 -51.427 -89.960 15.202 0.052 -0.038 -0.155 31.933 165.380 181.055 -46.548 0.008

185 87 5.129 6.196 -2.371 0.037 -0.073 -0.478 -10.174 193.861 142.269 -38.034 -0.196

186 85 0.046 0.120 8.887 0.049 -0.048 -0.285 23.437 198.978 164.813 -44.399 -0.093

187 98 -5.363 -118.215 2.297 0.106 0.043 0.517 169.758 228.806 272.700 -64.781 0.140

188 88 5.498 3.953 0.358 0.041 -0.045 -0.406 -54.264 199.602 155.281 -52.403 -0.042

189 88 0.024 0.179 1.320 0.073 0.004 0.132 116.625 234.402 207.325 -53.318 0.058

190 106 -102.861 -55.473 61.645 -50.622 185.860 6.663 0.302 -0.189 -0.642 -0.420 -0.578

191 89 5.142 7.710 1.921 -349.130 71.063 2.191 -0.015 -0.227 -2.120 -29.593 -0.200

192 98 0.066 0.107 39.009 -202.481 152.779 5.353 0.231 -0.233 -0.953 -9.816 -0.480

193 95 -67.749 -69.901 28.853 -399.880 24.989 -1.877 -0.052 -0.393 -2.873 -48.898 0.152

194 89 5.429 6.010 5.476 -404.972 47.223 1.395 0.005 -0.231 -2.503 -39.082 -0.119

195 90 0.053 0.100 21.009 -433.532 32.125 -0.418 0.036 -0.370 -2.633 -46.535 0.031

196 128 -75.761 -59.213 3.573 52.946 111.430 3.298 0.289 -0.449 -1.662 -20.666 -0.120

197 90 5.034 8.107 0.231 -370.816 67.066 1.505 -0.044 -0.268 -2.184 -32.084 -0.137

198 110 0.060 0.145 -0.269 -38.030 231.496 2.948 0.331 -0.554 0.137 -0.613 -0.301

199 93 -32.572 -105.281 -30.208 15.826 0.632 1.225 -0.102 -0.007 -3.587 -50.395 -0.022

200 89 4.548 6.880 -20.014 9.745 -5.218 -2.535 -0.058 -0.204 -3.099 -41.344 -0.042

201 88 0.034 0.146 -26.021 13.927 -1.767 -0.588 -0.046 -0.109 -3.299 -47.647 -0.037

202 89 -52.771 -89.431 11.285 11.397 -3.982 -1.632 -0.142 -0.122 -3.224 -39.873 -0.046

203 90 4.988 6.327 1.736 8.652 -6.743 -4.469 -0.011 -0.174 -2.806 -35.177 -0.154

204 88 0.049 0.108 8.916 10.349 -5.328 -2.752 -0.009 -0.198 -3.010 -40.162 -0.092

205 90 -42.193 -96.886 0.903 13.776 -1.427 0.166 -0.166 -0.116 -3.565 -47.160 0.023

206 88 5.033 6.010 0.375 8.794 -6.565 -3.298 -0.027 -0.224 -2.921 -38.645 -0.080

207 87 0.041 0.129 0.697 12.368 -3.806 -1.410 -0.037 -0.177 -3.175 -44.950 -0.025

208 122 -46.156 -71.743 72.545 0.153 0.029 -0.062 0.133 -0.099 -3.296 -32.009 -0.203

209 89 3.307 10.764 -10.636 0.045 -0.060 -0.198 -0.068 -0.112 -2.795 -35.857 -0.133

210 103 0.029 0.180 48.978 0.087 -0.052 -0.258 0.220 -0.047 -2.014 -23.990 -0.439

211 91 -45.613 -90.187 23.362 0.053 -0.026 0.067 -0.171 -0.161 -3.541 -49.058 0.086

212 89 4.654 6.804 3.911 0.039 -0.069 -0.329 -0.025 -0.139 -2.984 -38.827 -0.138

213 88 0.040 0.131 16.350 0.050 -0.041 -0.097 -0.087 -0.175 -3.258 -46.332 -0.019

214 118 -36.222 -79.414 4.127 0.203 0.062 0.031 -0.016 -0.200 -3.708 -104.716 0.053

215 88 3.789 8.362 0.759 0.049 -0.037 -0.126 -0.068 -0.166 -3.241 -46.678 -0.023

216 107 0.018 0.178 2.846 0.139 0.062 0.334 0.035 -0.215 -3.203 -87.021 0.103

217 105 -94.443 -60.153 56.491 -106.844 181.108 6.173 0.000 0.000 -0.008 4.517 -0.605

218 90 5.111 7.286 -5.923 -375.598 47.095 1.667 0.000 0.000 -0.012 -35.784 -0.142

219 97 0.061 0.113 33.633 -233.594 137.005 5.041 0.000 0.000 -0.008 -8.619 -0.467

220 93 -68.080 -73.241 22.488 -394.577 32.356 -1.171 0.000 0.000 -0.014 -43.509 0.081

221 90 5.436 5.969 1.149 -390.189 41.417 2.288 0.000 0.000 -0.011 -39.076 -0.160

222 90 0.052 0.106 15.368 -429.556 35.823 0.290 0.000 0.000 -0.013 -42.718 -0.022

223 123 -72.469 -65.638 1.588 78.592 217.247 1.718 -0.001 0.000 -0.013 1.625 -0.156

224 90 5.191 6.580 0.314 -397.264 38.297 1.279 0.000 0.000 -0.012 -39.982 -0.111

225 105 0.049 0.155 0.308 -152.312 195.362 1.181 -0.001 0.000 -0.010 0.929 -0.220

226 92 -38.684 -103.586 -24.858 14.007 -0.622 -0.540 0.000 0.000 -0.016 -46.564 -0.025

227 90 5.158 5.705 -13.439 8.202 -6.373 -3.669 0.000 0.000 -0.013 -40.740 -0.054

228 89 0.040 0.135 -19.911 11.991 -2.632 -2.259 0.000 0.000 -0.014 -45.701 -0.055

229 91 -57.067 -85.851 8.212 10.553 -4.148 -2.190 0.000 0.000 -0.014 -39.553 -0.060

230 90 5.066 6.598 -1.738 8.123 -6.829 -5.212 0.000 0.000 -0.012 -34.390 -0.186


231 89 0.047 0.121 4.651 10.092 -4.957 -3.898 0.000 0.000 -0.013 -39.603 -0.114

232 90 -48.779 -94.532 0.662 12.205 -2.298 -1.126 0.000 0.000 -0.015 -44.665 -0.003

233 90 5.327 5.566 0.150 7.602 -6.952 -4.743 0.000 0.000 -0.013 -37.710 -0.107

234 88 0.045 0.123 0.482 10.860 -4.117 -2.958 0.000 0.000 -0.014 -43.391 -0.072

235 120 -40.263 -82.021 51.911 0.145 0.018 -0.116 0.000 0.000 -0.017 -37.029 -0.217

236 89 3.723 8.823 -20.937 0.046 -0.037 -0.171 0.000 0.000 -0.014 -45.761 -0.043

237 102 0.021 0.218 34.572 0.066 -0.071 -0.289 0.000 0.000 -0.013 -15.496 -0.506

238 91 -46.233 -94.930 17.647 0.049 -0.032 -0.034 0.000 0.000 -0.016 -45.070 0.019

239 90 4.751 6.868 -0.783 0.037 -0.065 -0.444 0.000 0.000 -0.013 -38.922 -0.174

240 88 0.041 0.134 11.185 0.047 -0.038 -0.222 0.000 0.000 -0.014 -45.225 -0.065

241 114 -18.948 -99.670 3.180 0.153 0.065 0.330 0.000 0.000 -0.020 -90.068 0.147

242 90 4.969 5.465 0.419 0.040 -0.043 -0.343 0.000 0.000 -0.014 -49.163 -0.052

243 96 0.010 0.219 1.743 0.076 0.016 0.440 -0.001 0.000 -0.018 -53.444 0.098

App

endix

VI:

DR

AG

Est

imati

on

===============================================================================================================================

I.

BETA

TYPE

=LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

ELASTICITY

S(y)

(EP)

VARIANT

=M1

M2

M3

M4

M5

M6

M7

M8

M9

M10

(COND.

T-STATISTIC)

VERSION

=0

11

11

11

11

1

DEP.VAR.

=AC1

AC2

AC3

AC4

AC5

AC6

AC7

AC8

AC9

AC10

===============================================================================================================================

comtot

.10E+01

.96E+00

.95E+00

.98E+00

.13E+01

.89E+00

.88E+00

.91E+00

.12E+01

.83E+00

.284

.285

.278

.286

.282

.201

.279

.287

.283

.202

(1.63)

(1.63)

(1.60)

(1.64)

(1.61)

(1.15)

(1.60)

(1.65)

(1.62)

(1.16)

LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1

conalc

-.53E+01

-.50E+01

-.48E+01

-.51E+01

-.67E+01

-.64E+01

-.46E+01

-.48E+01

-.63E+01

-.61E+01

-.341

-.341

-.306

-.341

-.341

-.341

-.306

-.341

-.341

-.342

(-6.75)

(-6.75)

(-6.04)

(-6.76)

(-6.72)

(-6.77)

(-6.04)

(-6.76)

(-6.72)

(-6.77)

LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1

dlab

.65E+00

.59E+00

.56E+00

.60E+00

.60E+00

.80E+00

.51E+00

.54E+00

.55E+00

.73E+00

.812

.812

.815

.809

.633

.810

.815

.809

.633

.810

(5.35)

(5.35)

(5.36)

(5.33)

(4.17)

(5.33)

(5.35)

(5.33)

(4.17)

(5.33)

LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1

parser

-.17E+02

-.15E+02

-.18E+02

-.16E+02

-.22E+02

-.20E+02

-.16E+02

-.15E+02

-.20E+02

-.19E+02

-.624

-.600

-.625

-.624

-.628

-.622

-.601

-.599

-.604

-.597

(-5.04)

(-4.84)

(-5.04)

(-5.04)

(-5.09)

(-5.03)

(-4.84)

(-4.83)

(-4.89)

(-4.83)

LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1

rcp

-.29E-01

-.26E-01

-.23E-01

-.26E-01

-.33E-01

-.36E-01

-.21E-01

-.23E-01

-.30E-01

-.32E-01

===

-.094

-.094

-.093

-.094

-.095

-.094

-.094

-.094

-.095

-.095

(-2.16)

(-2.16)

(-2.15)

(-2.14)

(-2.17)

(-2.17)

(-2.15)

(-2.15)

(-2.18)

(-2.17)

susp

-.12E+01

-.11E+01

-.11E+01

-.94E+00

-.14E+01

-.14E+01

-.10E+01

-.88E+00

-.13E+01

-.13E+01

-.187

-.187

-.188

-.161

-.185

-.187

-.188

-.161

-.185

-.187

(-2.83)

(-2.84)

(-2.84)

(-2.44)

(-2.80)

(-2.84)

(-2.85)

(-2.44)

(-2.80)

(-2.84)

LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1

-------------------------------------------------------------------------------------------------------------------------------

REGRESSION

CONSTANT

CONSTANT

.70E+02

.64E+02

.68E+02

.66E+02

.88E+02

.85E+02

.62E+02

.61E+02

.80E+02

.78E+02

--

--

--

--

--

(7.17)

(6.96)

(6.96)

(7.11)

(7.17)

(7.18)

(6.76)

(6.91)

(6.96)

(6.97)

===============================================================================================================================

===============================================================================================================================

II.

PARAMETERS

TYPE

=LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

VARIANT

=M1

M2

M3

M4

M5

M6

M7

M8

M9

M10

(COND.

T-STATISTIC)

VERSION

=0

11

11

11

11

1

DEP.VAR.

=AC1

AC2

AC3

AC4

AC5

AC6

AC7

AC8

AC9

AC10

===============================================================================================================================

------------------------------------------------------------------

BOX-COX

TRANSFORMATIONS:

UNCOND:

[T-STATISTIC=0]

/[T-STATISTIC=1]

------------------------------------------------------------------

LAMBDA(Y)

-GROUP

1LAM

1-.317

-.321

-.335

-.322

-.324

-.316

-.340

-.326

-.329

-.320

[-1.73]

[-1.73]

[-1.67]

[-1.75]

[-1.69]

[-1.72]

[-1.67]

[-1.75]

[-1.69]

[-1.72]

[-7.19]

[-7.11]

[-6.67]

[-7.18]

[-6.92]

[-7.17]

[-6.59]

[-7.10]

[-6.84]

[-7.09]

LAMBDA(X)

-GROUP

1LAM

1-.317

-.321

-.335

-.322

-.324

-.316

-.340

-.326

-.329

-.320

[-1.73]

[-1.73]

[-1.67]

[-1.75]

[-1.69]

[-1.72]

[-1.67]

[-1.75]

[-1.69]

[-1.72]

[-7.19]

[-7.11]

[-6.67]

[-7.18]

[-6.92]

[-7.17]

[-6.59]

[-7.10]

[-6.84]

[-7.09]

---------------

AUTOCORRELATION

---------------

ORDER

1RHO

1.303

.303

.302

.303

.303

.302

.302

.303

.303

.303

(2.99)

(2.99)

(3.00)

(2.98)

(3.01)

(2.99)

(2.99)

(2.98)

(3.01)

(2.99)

ORDER

2RHO

2.168

.169

.166

.170

.166

.168

.166

.170

.167

.168

(1.57)

(1.57)

(1.55)

(1.58)

(1.55)

(1.56)

(1.55)

(1.59)

(1.55)

(1.56)

===============================================================================================================================

III.GENERAL

STATISTICS

TYPE

=LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

VARIANT

=M1

M2

M3

M4

M5

M6

M7

M8

M9

M10

VERSION

=0

11

11

11

11

1

DEP.VAR.

=AC1

AC2

AC3

AC4

AC5

AC6

AC7

AC8

AC9

AC10

===============================================================================================================================

LOG-LIKELIHOOD

-291.727

-326.398

-339.667

-321.721

-228.495

-214.177

-374.340

-356.392

-263.167

-248.849

PSEUDO-R2

:-

(E)

.933

.933

.928

.932

.932

.935

.927

.931

.932

.934

-(L)

.945

.944

.940

.943

.944

.947

.939

.942

.944

.946

-(E)

ADJUSTED

FOR

D.F.

.928

.927

.922

.926

.927

.930

.921

.925

.926

.929

-(L)

ADJUSTED

FOR

D.F.

.941

.940

.935

.939

.940

.943

.934

.938

.939

.942

AVERAGE

PROBABILITY

(Y=LIMIT

OBSERV.)

.000

.000

.000

.000

.000

.000

.000

.000

.000

.000

SAMPLE

:-

NUMBER

OF

OBSERVATIONS

118

118

118

118

118

118

118

118

118

118

-FIRST

OBSERVATION

33

33

33

33

33

-LAST

OBSERVATION

120

120

120

120

120

120

120

120

120

120

NUMBER

OF

ESTIMATED

PARAMETERS

:

-FIXED

PART

:

.BETAS

77

77

77

77

77

.BOX-COX

11

11

11

11

11

.ASSOCIATED

DUMMIES

00

00

00

00

00

-AUTOCORRELATION

22

22

22

22

22

-HETEROSKEDASTICITY

:

.DELTAS

00

00

00

00

00

.BOX-COX

00

00

00

00

00

.ASSOCIATED

DUMMIES

00

00

00

00

00

===============================================================================================================================

=================================================================================================================================================

I.

BETA

TYPE

=LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

ELASTICITY

S(y)

(EP)

VARIANT

=M11

M12

M13

M14

M15

M16

M17

M18

M19

M20

M21

M22

(COND.

T-STATISTIC)

VERSION

=1

11

11

11

11

11

1

DEP.VAR.

=AC11

AC12

AC13

AC14

AC15

AC16

AC17

AC18

AC19

AC20

AC21

AC22

=================================================================================================================================================

-----------

INDEPENDENT

-----------

comtot

.90E+00

.12E+01

.83E+00

.12E+01

.86E+00

.11E+01

.83E+00

.11E+01

.77E+00

.11E+01

.10E+01

.80E+00

.281

.276

.196

.285

.204

.198

.282

.277

.197

.286

.200

.205

(1.61)

(1.58)

(1.12)

(1.63)

(1.17)

(1.13)

(1.62)

(1.58)

(1.12)

(1.63)

(1.14)

(1.17)

LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1

conalc

-.47E+01

-.62E+01

-.60E+01

-.65E+01

-.62E+01

-.82E+01

-.44E+01

-.59E+01

-.57E+01

-.61E+01

-.78E+01

-.59E+01

-.307

-.306

-.307

-.341

-.342

-.341

-.307

-.306

-.307

-.341

-.342

-.342

(-6.05)

(-6.02)

(-6.07)

(-6.73)

(-6.79)

(-6.74)

(-6.05)

(-6.02)

(-6.07)

(-6.73)

(-6.74)

(-6.79)

LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1

dlab

.51E+00

.53E+00

.70E+00

.55E+00

.74E+00

.74E+00

.46E+00

.47E+00

.63E+00

.50E+00

.68E+00

.67E+00

.812

.637

.814

.630

.807

.632

.812

.637

.814

.630

.632

.807

(5.34)

(4.18)

(5.34)

(4.15)

(5.32)

(4.16)

(5.34)

(4.18)

(5.34)

(4.15)

(4.15)

(5.31)

LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1

parser

-.17E+02

-.23E+02

-.22E+02

-.21E+02

-.20E+02

-.26E+02

-.16E+02

-.21E+02

-.20E+02

-.19E+02

-.24E+02

-.18E+02

-.625

-.630

-.623

-.628

-.621

-.626

-.601

-.605

-.599

-.604

-.602

-.597

(-5.04)

(-5.09)

(-5.03)

(-5.09)

(-5.02)

(-5.08)

(-4.83)

(-4.89)

(-4.82)

(-4.88)

(-4.87)

(-4.82)

LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1

rcp

-.21E-01

-.27E-01

-.29E-01

-.30E-01

-.32E-01

-.42E-01

-.18E-01

-.24E-01

-.26E-01

-.27E-01

-.38E-01

-.29E-01

===

-.093

-.094

-.094

-.094

-.094

-.095

-.093

-.094

-.094

-.094

-.095

-.094

(-2.13)

(-2.16)

(-2.16)

(-2.16)

(-2.15)

(-2.18)

(-2.14)

(-2.17)

(-2.16)

(-2.16)

(-2.19)

(-2.16)

susp

-.92E+00

-.14E+01

-.14E+01

-.12E+01

-.12E+01

-.17E+01

-.85E+00

-.13E+01

-.13E+01

-.11E+01

-.16E+01

-.11E+01

-.162

-.185

-.188

-.158

-.161

-.185

-.162

-.186

-.188

-.158

-.185

-.161

(-2.44)

(-2.81)

(-2.84)

(-2.40)

(-2.44)

(-2.80)

(-2.45)

(-2.81)

(-2.85)

(-2.41)

(-2.81)

(-2.44)

LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1

-------------------------------------------------------------------------------------------------------------------------------------------------

REGRESSION

CONSTANT

CONSTANT

.65E+02

.87E+02

.85E+02

.84E+02

.82E+02

.11E+03

.59E+02

.80E+02

.77E+02

.77E+02

.99E+02

.75E+02

--

--

--

--

--

--

(6.91)

(6.96)

(6.97)

(7.11)

(7.12)

(7.20)

(6.70)

(6.75)

(6.76)

(6.90)

(6.99)

(6.91)

=================================================================================================================================================

=================================================================================================================================================

II.

PARAMETERS

TYPE

=LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

VARIANT

=M11

M12

M13

M14

M15

M16

M17

M18

M19

M20

M21

M22

(COND.

T-STATISTIC)

VERSION

=1

11

11

11

11

11

1

DEP.VAR.

=AC11

AC12

AC13

AC14

AC15

AC16

AC17

AC18

AC19

AC20

AC21

AC22

=================================================================================================================================================

------------------------------------------------------------------

BOX-COX

TRANSFORMATIONS:

UNCOND:

[T-STATISTIC=0]

/[T-STATISTIC=1]

------------------------------------------------------------------

LAMBDA(Y)

-GROUP

1LAM

1-.341

-.344

-.334

-.330

-.321

-.323

-.346

-.349

-.339

-.335

-.327

-.325

[-1.69]

[-1.64]

[-1.66]

[-1.72]

[-1.74]

[-1.68]

[-1.69]

[-1.64]

[-1.66]

[-1.71]

[-1.68]

[-1.74]

[-6.65]

[-6.41]

[-6.65]

[-6.91]

[-7.16]

[-6.90]

[-6.58]

[-6.33]

[-6.57]

[-6.83]

[-6.82]

[-7.08]

LAMBDA(X)

-GROUP

1LAM

1-.341

-.344

-.334

-.330

-.321

-.323

-.346

-.349

-.339

-.335

-.327

-.325

[-1.69]

[-1.64]

[-1.66]

[-1.72]

[-1.74]

[-1.68]

[-1.69]

[-1.64]

[-1.66]

[-1.71]

[-1.68]

[-1.74]

[-6.65]

[-6.41]

[-6.65]

[-6.91]

[-7.16]

[-6.90]

[-6.58]

[-6.33]

[-6.57]

[-6.83]

[-6.82]

[-7.08]

---------------

AUTOCORRELATION

---------------

ORDER

1RHO

1.302

.303

.302

.303

.303

.303

.302

.303

.302

.303

.303

.303

(2.99)

(3.01)

(2.99)

(3.00)

(2.98)

(3.01)

(2.99)

(3.01)

(2.99)

(3.00)

(3.01)

(2.98)

ORDER

2RHO

2.167

.164

.165

.168

.169

.166

.168

.164

.166

.169

.166

.170

(1.56)

(1.53)

(1.54)

(1.56)

(1.57)

(1.54)

(1.57)

(1.53)

(1.54)

(1.57)

(1.55)

(1.58)

=================================================================================================================================================

III.GENERAL

STATISTICS

TYPE

=LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

VARIANT

=M11

M12

M13

M14

M15

M16

M17

M18

M19

M20

M21

M22

VERSION

=1

11

11

11

11

11

1

DEP.VAR.

=AC11

AC12

AC13

AC14

AC15

AC16

AC17

AC18

AC19

AC20

AC21

AC22

=================================================================================================================================================

LOG-LIKELIHOOD

-369.659

-276.433

-262.116

-258.485

-244.170

-150.950

-404.331

-311.107

-296.790

-293.157

-185.623

-278.842

PSEUDO-R2

:-

(E)

.926

.927

.930

.930

.933

.934

.925

.926

.929

.930

.933

.932

-(L)

.938

.939

.942

.942

.945

.946

.937

.938

.941

.941

.945

.944

-(E)

ADJUSTED

FOR

D.F.

.920

.921

.924

.925

.928

.929

.919

.920

.923

.924

.928

.927

-(L)

ADJUSTED

FOR

D.F.

.933

.934

.937

.938

.941

.942

.931

.933

.936

.937

.941

.940

AVERAGE

PROBABILITY

(Y=LIMIT

OBSERV.)

.000

.000

.000

.000

.000

.000

.000

.000

.000

.000

.000

.000

SAMPLE

:-

NUMBER

OF

OBSERVATIONS

118

118

118

118

118

118

118

118

118

118

118

118

-FIRST

OBSERVATION

33

33

33

33

33

33

-LAST

OBSERVATION

120

120

120

120

120

120

120

120

120

120

120

120

NUMBER

OF

ESTIMATED

PARAMETERS

:

-FIXED

PART

:

.BETAS

77

77

77

77

77

77

.BOX-COX

11

11

11

11

11

11

.ASSOCIATED

DUMMIES

00

00

00

00

00

00

-AUTOCORRELATION

22

22

22

22

22

22

-HETEROSKEDASTICITY

:

.DELTAS

00

00

00

00

00

00

.BOX-COX

00

00

00

00

00

00

.ASSOCIATED

DUMMIES

00

00

00

00

00

00

=================================================================================================================================================

===============================================================================================================================

I.

BETA

TYPE

=LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

ELASTICITY

S(y)

(EP)

VARIANT

=M23

M24

M25

M26

M27

M28

M29

M30

M31

M32

(COND.

T-STATISTIC)

VERSION

=1

11

11

21

11

1

DEP.VAR.

=AC23

AC24

AC25

AC27

AC27

AC28

AC29

AC30

AC31

AC32

===============================================================================================================================

-----------

INDEPENDENT

-----------

comtot

.11E+01

.79E+00

.10E+01

.10E+01

.10E+01

.74E+00

.98E+00

.97E+00

.95E+00

.91E+00

.279

.199

.193

.280

.280

.200

.196

.203

.194

.197

(1.60)

(1.14)

(1.10)

(1.60)

(1.60)

(1.14)

(1.12)

(1.16)

(1.11)

(1.13)

LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1

conalc

-.61E+01

-.58E+01

-.77E+01

-.57E+01

-.57E+01

-.55E+01

-.76E+01

-.76E+01

-.73E+01

-.72E+01

-.307

-.307

-.307

-.307

-.307

-.307

-.307

-.342

-.307

-.308

(-6.03)

(-6.08)

(-6.04)

(-6.03)

(-6.03)

(-6.08)

(-6.05)

(-6.75)

(-6.04)

(-6.05)

LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1

dlab

.48E+00

.64E+00

.66E+00

.43E+00

.43E+00

.58E+00

.60E+00

.62E+00

.59E+00

.54E+00

.633

.811

.635

.633

.633

.810

.632

.629

.635

.632

(4.16)

(5.33)

(4.17)

(4.16)

(4.16)

(5.32)

(4.15)

(4.14)

(4.17)

(4.15)

LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1

parser

-.23E+02

-.21E+02

-.29E+02

-.21E+02

-.21E+02

-.20E+02

-.28E+02

-.24E+02

-.26E+02

-.26E+02

-.630

-.623

-.627

-.606

-.606

-.598

-.627

-.602

-.603

-.603

(-5.09)

(-5.02)

(-5.08)

(-4.89)

(-4.89)

(-4.82)

(-5.07)

(-4.87)

(-4.87)

(-4.87)

LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1

rcp

-.24E-01

-.26E-01

-.34E-01

-.21E-01

-.21E-01

-.23E-01

-.31E-01

-.34E-01

-.31E-01

-.27E-01

===

-.093

-.093

-.094

-.094

-.094

-.093

-.094

-.095

-.094

-.094

(-2.15)

(-2.14)

(-2.17)

(-2.15)

(-2.15)

(-2.15)

(-2.16)

(-2.17)

(-2.18)

(-2.16)

susp

-.11E+01

-.11E+01

-.17E+01

-.11E+01

-.11E+01

-.11E+01

-.14E+01

-.13E+01

-.16E+01

-.13E+01

-.159

-.162

-.185

-.159

-.159

-.162

-.159

-.159

-.186

-.159

(-2.41)

(-2.45)

(-2.81)

(-2.41)

(-2.41)

(-2.45)

(-2.41)

(-2.41)

(-2.81)

(-2.42)

LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1

-------------------------------------------------------------------------------------------------------------------------------

REGRESSION

CONSTANT

CONSTANT

.84E+02

.81E+02

.11E+03

.76E+02

.76E+02

.74E+02

.10E+03

.95E+02

.99E+02

.95E+02

--

--

--

--

--

(6.90)

(6.91)

(6.98)

(6.69)

(6.69)

(6.70)

(6.92)

(6.92)

(6.76)

(6.70)

===============================================================================================================================

===============================================================================================================================

II.

PARAMETERS

TYPE

=LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

VARIANT

=M23

M24

M25

M26

M27

M28

M29

M30

M31

M32

(COND.

T-STATISTIC)

VERSION

=1

11

11

21

11

1

DEP.VAR.

=AC23

AC24

AC25

AC27

AC27

AC28

AC29

AC30

AC31

AC32

===============================================================================================================================

------------------------------------------------------------------

BOX-COX

TRANSFORMATIONS:

UNCOND:

[T-STATISTIC=0]

/[T-STATISTIC=1]

------------------------------------------------------------------

LAMBDA(Y)

-GROUP

1LAM

1-.351

-.340

-.342

-.356

-.356

-.345

-.349

-.333

-.347

-.354

[-1.66]

[-1.68]

[-1.63]

[-1.66]

[-1.66]

[-1.68]

[-1.65]

[-1.70]

[-1.63]

[-1.65]

[-6.40]

[-6.63]

[-6.39]

[-6.33]

[-6.33]

[-6.56]

[-6.38]

[-6.81]

[-6.32]

[-6.30]

LAMBDA(X)

-GROUP

1LAM

1-.351

-.340

-.342

-.356

-.356

-.345

-.349

-.333

-.347

-.354

[-1.66]

[-1.68]

[-1.63]

[-1.66]

[-1.66]

[-1.68]

[-1.65]

[-1.70]

[-1.63]

[-1.65]

[-6.40]

[-6.63]

[-6.39]

[-6.33]

[-6.33]

[-6.56]

[-6.38]

[-6.81]

[-6.32]

[-6.30]

---------------

AUTOCORRELATION

---------------

ORDER

1RHO

1.303

.302

.303

.303

.303

.302

.303

.303

.303

.303

(3.00)

(2.98)

(3.01)

(3.00)

(3.00)

(2.98)

(3.00)

(3.00)

(3.01)

(3.00)

ORDER

2RHO

2.166

.167

.163

.166

.166

.167

.165

.168

.164

.166

(1.54)

(1.56)

(1.52)

(1.55)

(1.55)

(1.56)

(1.54)

(1.56)

(1.52)

(1.54)

===============================================================================================================================

III.GENERAL

STATISTICS

TYPE

=LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

VARIANT

=M23

M24

M25

M26

M27

M28

M29

M30

M31

M32

VERSION

=1

11

11

21

11

1

DEP.VAR.

=AC23

AC24

AC25

AC27

AC27

AC28

AC29

AC30

AC31

AC32

===============================================================================================================================

LOG-LIKELIHOOD

-306.421

-292.107

-198.888

-341.094

-341.094

-326.780

-228.874

-215.612

-233.562

-263.548

PSEUDO-R2

:-

(E)

.925

.928

.929

.924

.924

.927

.927

.931

.928

.926

-(L)

.937

.940

.941

.936

.936

.939

.939

.943

.940

.938

-(E)

ADJUSTED

FOR

D.F.

.919

.922

.923

.917

.917

.921

.921

.926

.922

.919

-(L)

ADJUSTED

FOR

D.F.

.931

.935

.936

.930

.930

.934

.934

.939

.935

.932

AVERAGE

PROBABILITY

(Y=LIMIT

OBSERV.)

.000

.000

.000

.000

.000

.000

.000

.000

.000

.000

SAMPLE

:-

NUMBER

OF

OBSERVATIONS

118

118

118

118

118

118

118

118

118

118

-FIRST

OBSERVATION

33

33

33

33

33

-LAST

OBSERVATION

120

120

120

120

120

120

120

120

120

120

NUMBER

OF

ESTIMATED

PARAMETERS

:

-FIXED

PART

:

.BETAS

77

77

77

77

77

.BOX-COX

11

11

11

11

11

.ASSOCIATED

DUMMIES

00

00

00

00

00

-AUTOCORRELATION

22

22

22

22

22

-HETEROSKEDASTICITY

:

.DELTAS

00

00

00

00

00

.BOX-COX

00

00

00

00

00

.ASSOCIATED

DUMMIES

00

00

00

00

00

===============================================================================================================================

===============================================================================================================================

I.

BETA

TYPE

=LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

ELASTICITY

S(y)

(EP)

VARIANT

=M33

M34

M35

M36

M37

M38

M39

M40

M41

M42

(COND.

T-STATISTIC)

VERSION

=1

11

11

11

11

1

DEP.VAR.

=AC33

AC34

AC35

AC36

AC37

AC38

AC39

AC40

AC41

AC42

===============================================================================================================================

-----------

INDEPENDENT

-----------

comtot

.40E+00

.41E+00

.38E+00

.43E+00

.34E+00

.31E+00

.39E+00

.44E+00

.35E+00

.32E+00

.629

.629

.630

.630

.627

.543

.630

.630

.627

.543

(3.80)

(3.80)

(3.83)

(3.80)

(3.81)

(3.29)

(3.83)

(3.80)

(3.81)

(3.29)

LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1

conalc

-.72E-01

-.72E-01

-.50E-01

-.82E-01

-.56E-01

-.63E-01

-.49E-01

-.82E-01

-.56E-01

-.63E-01

-.200

-.200

-.167

-.200

-.199

-.200

-.167

-.200

-.199

-.199

(-4.28)

(-4.28)

(-3.60)

(-4.27)

(-4.29)

(-4.27)

(-3.61)

(-4.27)

(-4.29)

(-4.27)

LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1

dlab

.90E+00

.94E+00

.99E+00

.91E+00

.66E+00

.83E+00

.11E+01

.95E+00

.69E+00

.87E+00

.779

.779

.779

.777

.606

.781

.780

.777

.606

.781

(5.31)

(5.31)

(5.32)

(5.29)

(4.13)

(5.32)

(5.33)

(5.29)

(4.14)

(5.33)

LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1

parser

-.29E-01

-.24E-01

-.22E-01

-.35E-01

-.22E-01

-.25E-01

-.18E-01

-.28E-01

-.17E-01

-.20E-01

-.102

-.081

-.099

-.103

-.099

-.101

-.079

-.083

-.079

-.081

(-1.05)

(-.84)

(-1.03)

(-1.07)

(-1.03)

(-1.05)

(-.82)

(-.86)

(-.82)

(-.84)

LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1

rcp

-.75E-01

-.80E-01

-.92E-01

-.74E-01

-.76E-01

-.71E-01

-.99E-01

-.78E-01

-.81E-01

-.75E-01

===

-.045

-.045

-.045

-.045

-.045

-.045

-.045

-.045

-.045

-.045

(-1.15)

(-1.15)

(-1.16)

(-1.15)

(-1.15)

(-1.15)

(-1.16)

(-1.15)

(-1.15)

(-1.15)

susp

-.55E-01

-.56E-01

-.50E-01

-.44E-01

-.47E-01

-.49E-01

-.51E-01

-.45E-01

-.47E-01

-.50E-01

-.107

-.107

-.108

-.079

-.109

-.107

-.108

-.079

-.109

-.108

(-1.84)

(-1.84)

(-1.86)

(-1.35)

(-1.87)

(-1.85)

(-1.86)

(-1.35)

(-1.87)

(-1.85)

LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1

-------------------------------------------------------------------------------------------------------------------------------

REGRESSION

CONSTANT

CONSTANT

.11E+01

.12E+01

.11E+01

.12E+01

.12E+01

.10E+01

.12E+01

.13E+01

.13E+01

.11E+01

--

--

--

--

--

(.80)

(.84)

(.76)

(.84)

(.92)

(.81)

(.78)

(.87)

(.99)

(.87)

===============================================================================================================================

===============================================================================================================================

II.

PARAMETERS

TYPE

=LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

VARIANT

=M33

M34

M35

M36

M37

M38

M39

M40

M41

M42

(COND.

T-STATISTIC)

VERSION

=1

11

11

11

11

1

DEP.VAR.

=AC33

AC34

AC35

AC36

AC37

AC38

AC39

AC40

AC41

AC42

===============================================================================================================================

------------------------------------------------------------------

BOX-COX

TRANSFORMATIONS:

UNCOND:

[T-STATISTIC=0]

/[T-STATISTIC=1]

------------------------------------------------------------------

LAMBDA(Y)

-GROUP

1LAM

1.125

.129

.156

.113

.145

.130

.162

.117

.150

.134

[.35]

[.35]

[.37]

[.31]

[.38]

[.36]

[.38]

[.32]

[.39]

[.37]

[-2.43]

[-2.38]

[-2.01]

[-2.46]

[-2.26]

[-2.41]

[-1.95]

[-2.41]

[-2.22]

[-2.37]

LAMBDA(X)

-GROUP

1LAM

1.125

.129

.156

.113

.145

.130

.162

.117

.150

.134

[.35]

[.35]

[.37]

[.31]

[.38]

[.36]

[.38]

[.32]

[.39]

[.37]

[-2.43]

[-2.38]

[-2.01]

[-2.46]

[-2.26]

[-2.41]

[-1.95]

[-2.41]

[-2.22]

[-2.37]

---------------

AUTOCORRELATION

---------------

ORDER

1RHO

1.157

.156

.157

.157

.156

.156

.156

.157

.156

.156

(1.46)

(1.46)

(1.46)

(1.47)

(1.46)

(1.46)

(1.46)

(1.47)

(1.45)

(1.46)

ORDER

2RHO

2.247

.247

.248

.248

.247

.247

.248

.248

.247

.247

(2.65)

(2.65)

(2.65)

(2.65)

(2.65)

(2.65)

(2.65)

(2.65)

(2.65)

(2.65)

===============================================================================================================================

III.GENERAL

STATISTICS

TYPE

=LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

VARIANT

=M33

M34

M35

M36

M37

M38

M39

M40

M41

M42

VERSION

=1

11

11

11

11

1

DEP.VAR.

=AC33

AC34

AC35

AC36

AC37

AC38

AC39

AC40

AC41

AC42

===============================================================================================================================

LOG-LIKELIHOOD

-344.630

-379.310

-392.413

-374.689

-281.329

-267.066

-427.091

-409.370

-316.009

-301.746

PSEUDO-R2

:-

(E)

.772

.766

.744

.765

.759

.774

.736

.758

.751

.767

-(L)

.775

.768

.747

.767

.761

.776

.739

.760

.754

.769

-(E)

ADJUSTED

FOR

D.F.

.753

.746

.723

.745

.739

.755

.715

.738

.730

.747

-(L)

ADJUSTED

FOR

D.F.

.756

.749

.726

.748

.741

.757

.717

.740

.733

.750

AVERAGE

PROBABILITY

(Y=LIMIT

OBSERV.)

.000

.000

.000

.000

.000

.000

.000

.000

.000

.000

SAMPLE

:-

NUMBER

OF

OBSERVATIONS

118

118

118

118

118

118

118

118

118

118

-FIRST

OBSERVATION

33

33

33

33

33

-LAST

OBSERVATION

120

120

120

120

120

120

120

120

120

120

NUMBER

OF

ESTIMATED

PARAMETERS

:

-FIXED

PART

:

.BETAS

77

77

77

77

77

.BOX-COX

11

11

11

11

11

.ASSOCIATED

DUMMIES

00

00

00

00

00

-AUTOCORRELATION

22

22

22

22

22

-HETEROSKEDASTICITY

:

.DELTAS

00

00

00

00

00

.BOX-COX

00

00

00

00

00

.ASSOCIATED

DUMMIES

00

00

00

00

00

===============================================================================================================================

===============================================================================================================================

I.

BETA

TYPE

=LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

ELASTICITY

S(y)

(EP)

VARIANT

=M43

M44

M45

M46

M47

M48

M49

M50

M51

M52

(COND.

T-STATISTIC)

VERSION

=1

12

11

11

11

1

DEP.VAR.

=AC43

AC44

AC45

AC46

AC47

AC48

AC49

AC50

AC51

AC52

===============================================================================================================================

-----------

INDEPENDENT

-----------

comtot

.41E+00

.32E+00

.29E+00

.37E+00

.34E+00

.26E+00

.42E+00

.33E+00

.30E+00

.38E+00

.631

.629

.544

.629

.545

.541

.631

.628

.544

.628

(3.82)

(3.84)

(3.31)

(3.80)

(3.29)

(3.29)

(3.83)

(3.84)

(3.32)

(3.81)

LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1

conalc

-.57E-01

-.37E-01

-.42E-01

-.65E-01

-.72E-01

-.48E-01

-.57E-01

-.37E-01

-.41E-01

-.65E-01

-.167

-.166

-.167

-.200

-.200

-.199

-.167

-.166

-.166

-.200

(-3.60)

(-3.61)

(-3.60)

(-4.28)

(-4.27)

(-4.28)

(-3.60)

(-3.62)

(-3.60)

(-4.28)

LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1

dlab

.10E+01

.73E+00

.90E+00

.68E+00

.85E+00

.60E+00

.11E+01

.77E+00

.95E+00

.71E+00

.778

.606

.781

.604

.779

.608

.778

.606

.782

.604

(5.30)

(4.14)

(5.34)

(4.11)

(5.30)

(4.15)

(5.31)

(4.15)

(5.35)

(4.12)

LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1

parser

-.27E-01

-.16E-01

-.18E-01

-.26E-01

-.30E-01

-.18E-01

-.21E-01

-.12E-01

-.15E-01

-.21E-01

-.101

-.097

-.099

-.101

-.103

-.099

-.081

-.077

-.078

-.081

(-1.05)

(-1.01)

(-1.03)

(-1.05)

(-1.07)

(-1.03)

(-.84)

(-.80)

(-.82)

(-.84)

LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1

rcp

-.90E-01

-.93E-01

-.86E-01

-.75E-01

-.70E-01

-.71E-01

-.97E-01

-.10E+00

-.93E-01

-.80E-01

===

-.045

-.045

-.045

-.045

-.045

-.045

-.045

-.045

-.045

-.045

(-1.16)

(-1.16)

(-1.16)

(-1.16)

(-1.15)

(-1.16)

(-1.16)

(-1.16)

(-1.16)

(-1.16)

susp

-.41E-01

-.41E-01

-.44E-01

-.38E-01

-.40E-01

-.41E-01

-.42E-01

-.42E-01

-.44E-01

-.39E-01

-.080

-.110

-.109

-.080

-.079

-.109

-.080

-.110

-.109

-.080

(-1.37)

(-1.89)

(-1.87)

(-1.38)

(-1.36)

(-1.88)

(-1.37)

(-1.89)

(-1.87)

(-1.38)

LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1

-------------------------------------------------------------------------------------------------------------------------------

REGRESSION

CONSTANT

CONSTANT

.12E+01

.13E+01

.11E+01

.13E+01

.11E+01

.10E+01

.13E+01

.14E+01

.12E+01

.14E+01

--

--

--

--

--

(.78)

(.95)

(.80)

(.95)

(.86)

(.90)

(.79)

(1.01)

(.85)

(1.00)

===============================================================================================================================

===============================================================================================================================

II.

PARAMETERS

TYPE

=LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

VARIANT

=M43

M44

M45

M46

M47

M48

M49

M50

M51

M52

(COND.

T-STATISTIC)

VERSION

=1

12

11

11

11

1

DEP.VAR.

=AC43

AC44

AC45

AC46

AC47

AC48

AC49

AC50

AC51

AC52

===============================================================================================================================

------------------------------------------------------------------

BOX-COX

TRANSFORMATIONS:

UNCOND:

[T-STATISTIC=0]

/[T-STATISTIC=1]

------------------------------------------------------------------

LAMBDA(Y)

-GROUP

1LAM

1.143

.179

.164

.132

.118

.152

.149

.186

.170

.137

[.34]

[.40]

[.39]

[.35]

[.33]

[.40]

[.35]

[.41]

[.40]

[.36]

[-2.03]

[-1.85]

[-1.98]

[-2.30]

[-2.45]

[-2.25]

[-1.98]

[-1.81]

[-1.93]

[-2.25]

LAMBDA(X)

-GROUP

1LAM

1.143

.179

.164

.132

.118

.152

.149

.186

.170

.137

[.34]

[.40]

[.39]

[.35]

[.33]

[.40]

[.35]

[.41]

[.40]

[.36]

[-2.03]

[-1.85]

[-1.98]

[-2.30]

[-2.45]

[-2.25]

[-1.98]

[-1.81]

[-1.93]

[-2.25]

---------------

AUTOCORRELATION

---------------

ORDER

1RHO

1.157

.156

.156

.157

.157

.155

.157

.156

.156

.156

(1.47)

(1.46)

(1.46)

(1.46)

(1.47)

(1.45)

(1.47)

(1.45)

(1.46)

(1.46)

ORDER

2RHO

2.248

.248

.247

.247

.247

.247

.248

.248

.247

.247

(2.65)

(2.65)

(2.65)

(2.65)

(2.64)

(2.65)

(2.65)

(2.65)

(2.65)

(2.65)

===============================================================================================================================

III.GENERAL

STATISTICS

TYPE

=LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

VARIANT

=M43

M44

M45

M46

M47

M48

M49

M50

M51

M52

VERSION

=1

12

11

11

11

1

DEP.VAR.

=AC43

AC44

AC45

AC46

AC47

AC48

AC49

AC50

AC51

AC52

===============================================================================================================================

LOG-LIKELIHOOD

-422.474

-329.113

-314.847

-311.392

-297.127

-203.763

-457.153

-363.791

-349.525

-346.072

PSEUDO-R2

:-

(E)

.736

.727

.744

.750

.765

.761

.728

.718

.736

.742

-(L)

.738

.730

.746

.752

.767

.763

.730

.721

.738

.744

-(E)

ADJUSTED

FOR

D.F.

.714

.705

.722

.729

.746

.741

.706

.695

.714

.720

-(L)

ADJUSTED

FOR

D.F.

.717

.707

.725

.731

.748

.744

.708

.698

.716

.723

AVERAGE

PROBABILITY

(Y=LIMIT

OBSERV.)

.000

.000

.000

.000

.000

.000

.000

.000

.000

.000

SAMPLE

:-

NUMBER

OF

OBSERVATIONS

118

118

118

118

118

118

118

118

118

118

-FIRST

OBSERVATION

33

33

33

33

33

-LAST

OBSERVATION

120

120

120

120

120

120

120

120

120

120

NUMBER

OF

ESTIMATED

PARAMETERS

:

-FIXED

PART

:

.BETAS

77

77

77

77

77

.BOX-COX

11

11

11

11

11

.ASSOCIATED

DUMMIES

00

00

00

00

00

-AUTOCORRELATION

22

22

22

22

22

-HETEROSKEDASTICITY

:

.DELTAS

00

00

00

00

00

.BOX-COX

00

00

00

00

00

.ASSOCIATED

DUMMIES

00

00

00

00

00

===============================================================================================================================

=================================================================================================================================================

I.

BETA

TYPE

=LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

ELASTICITY

S(y)

(EP)

VARIANT

=M53

M54

M55

M56

M57

M58

M59

M60

M61

M62

M63

M64

(COND.

T-STATISTIC)

VERSION

=1

11

11

11

11

11

1

DEP.VAR.

=AC53

AC54

AC55

AC56

AC57

AC58

AC59

AC60

AC61

AC62

AC63

AC64

=================================================================================================================================================

-----------

INDEPENDENT

-----------

comtot

.27E+00

.35E+00

.35E+00

.32E+00

.24E+00

.29E+00

.36E+00

.32E+00

.26E+00

.29E+00

.29E+00

.27E+00

.541

.545

.630

.545

.543

.543

.629

.545

.544

.543

.543

.543

(3.29)

(3.29)

(3.83)

(3.31)

(3.32)

(3.29)

(3.83)

(3.31)

(3.32)

(3.29)

(3.29)

(3.32)

LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1

conalc

-.48E-01

-.73E-01

-.44E-01

-.49E-01

-.30E-01

-.56E-01

-.44E-01

-.49E-01

-.36E-01

-.56E-01

-.56E-01

-.36E-01

-.199

-.200

-.167

-.167

-.166

-.199

-.167

-.167

-.166

-.199

-.199

-.166

(-4.28)

(-4.27)

(-3.61)

(-3.59)

(-3.61)

(-4.28)

(-3.61)

(-3.60)

(-3.60)

(-4.28)

(-4.28)

(-3.60)

LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1

dlab

.63E+00

.88E+00

.74E+00

.93E+00

.65E+00

.62E+00

.79E+00

.98E+00

.67E+00

.65E+00

.65E+00

.71E+00

.608

.779

.605

.780

.608

.606

.605

.780

.607

.606

.606

.607

(4.15)

(5.30)

(4.13)

(5.32)

(4.17)

(4.13)

(4.13)

(5.32)

(4.15)

(4.13)

(4.13)

(4.15)

LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1

parser

-.14E-01

-.24E-01

-.20E-01

-.22E-01

-.13E-01

-.22E-01

-.15E-01

-.18E-01

-.16E-01

-.18E-01

-.18E-01

-.12E-01

-.079

-.083

-.099

-.101

-.096

-.101

-.079

-.080

-.098

-.081

-.081

-.078

(-.82)

(-.86)

(-1.03)

(-1.05)

(-1.00)

(-1.05)

(-.82)

(-.84)

(-1.02)

(-.84)

(-.84)

(-.82)

LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1

rcp

-.75E-01

-.74E-01

-.92E-01

-.85E-01

-.86E-01

-.70E-01

-.99E-01

-.91E-01

-.85E-01

-.74E-01

-.74E-01

-.92E-01

===

-.045

-.045

-.045

-.045

-.045

-.045

-.045

-.045

-.045

-.045

-.045

-.045

(-1.16)

(-1.15)

(-1.16)

(-1.16)

(-1.16)

(-1.16)

(-1.16)

(-1.16)

(-1.16)

(-1.16)

(-1.16)

(-1.16)

susp

-.41E-01

-.41E-01

-.35E-01

-.36E-01

-.35E-01

-.34E-01

-.35E-01

-.37E-01

-.30E-01

-.35E-01

-.35E-01

-.30E-01

-.109

-.079

-.081

-.080

-.111

-.081

-.081

-.080

-.082

-.081

-.081

-.082

(-1.88)

(-1.36)

(-1.40)

(-1.38)

(-1.90)

(-1.39)

(-1.40)

(-1.38)

(-1.41)

(-1.39)

(-1.39)

(-1.41)

LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1LAM

1

-------------------------------------------------------------------------------------------------------------------------------------------------

REGRESSION

CONSTANT

CONSTANT

.12E+01

.12E+01

.14E+01

.11E+01

.12E+01

.11E+01

.15E+01

.13E+01

.13E+01

.13E+01

.13E+01

.14E+01

--

--

--

--

--

--

(.99)

(.91)

(.96)

(.83)

(.98)

(.95)

(1.01)

(.87)

(1.00)

(1.02)

(1.02)

(1.08)

=================================================================================================================================================

=================================================================================================================================================

II.

PARAMETERS

TYPE

=LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

VARIANT

=M53

M54

M55

M56

M57

M58

M59

M60

M61

M62

M63

M64

(COND.

T-STATISTIC)

VERSION

=1

11

11

11

11

11

1

DEP.VAR.

=AC53

AC54

AC55

AC56

AC57

AC58

AC59

AC60

AC61

AC62

AC63

AC64

=================================================================================================================================================

------------------------------------------------------------------

BOX-COX

TRANSFORMATIONS:

UNCOND:

[T-STATISTIC=0]

/[T-STATISTIC=1]

------------------------------------------------------------------

LAMBDA(Y)

-GROUP

1LAM

1.156

.122

.165

.151

.189

.139

.172

.156

.175

.143

.143

.181

[.41]

[.33]

[.37]

[.36]

[.43]

[.37]

[.38]

[.36]

[.39]

[.37]

[.37]

[.40]

[-2.20]

[-2.40]

[-1.88]

[-2.00]

[-1.82]

[-2.28]

[-1.83]

[-1.96]

[-1.85]

[-2.24]

[-2.24]

[-1.81]

LAMBDA(X)

-GROUP

1LAM

1.156

.122

.165

.151

.189

.139

.172

.156

.175

.143

.143

.181

[.41]

[.33]

[.37]

[.36]

[.43]

[.37]

[.38]

[.36]

[.39]

[.37]

[.37]

[.40]

[-2.20]

[-2.40]

[-1.88]

[-2.00]

[-1.82]

[-2.28]

[-1.83]

[-1.96]

[-1.85]

[-2.24]

[-2.24]

[-1.81]

---------------

AUTOCORRELATION

---------------

ORDER

1RHO

1.155

.157

.157

.157

.155

.156

.156

.157

.156

.156

.156

.156

(1.45)

(1.47)

(1.46)

(1.47)

(1.45)

(1.46)

(1.46)

(1.46)

(1.46)

(1.46)

(1.46)

(1.46)

ORDER

2RHO

2.247

.247

.248

.248

.247

.247

.248

.247

.247

.247

.247

.247

(2.65)

(2.64)

(2.65)

(2.65)

(2.65)

(2.65)

(2.65)

(2.65)

(2.65)

(2.65)

(2.65)

(2.65)

=================================================================================================================================================

III.GENERAL

STATISTICS

TYPE

=LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

LEVEL-1

VARIANT

=M53

M54

M55

M56

M57

M58

M59

M60

M61

M62

M63

M64

VERSION

=1

11

11

11

11

11

1

DEP.VAR.

=AC53

AC54

AC55

AC56

AC57

AC58

AC59

AC60

AC61

AC62

AC63

AC64

=================================================================================================================================================

LOG-LIKELIHOOD

-238.443

-331.808

-359.178

-344.910

-251.544

-233.828

-393.856

-379.590

-281.611

-268.508

-268.508

-316.290

PSEUDO-R2

:-

(E)

.753

.758

.718

.735

.728

.751

.708

.726

.717

.743

.743

.707

-(L)

.756

.760

.720

.737

.730

.753

.711

.729

.719

.745

.745

.709

-(E)

ADJUSTED

FOR

D.F.

.733

.738

.694

.713

.705

.730

.684

.704

.693

.722

.722

.683

-(L)

ADJUSTED

FOR

D.F.

.735

.740

.696

.715

.707

.733

.686

.706

.695

.724

.724

.685

AVERAGE

PROBABILITY

(Y=LIMIT

OBSERV.)

.000

.000

.000

.000

.000

.000

.000

.000

.000

.000

.000

.000

SAMPLE

:-

NUMBER

OF

OBSERVATIONS

118

118

118

118

118

118

118

118

118

118

118

118

-FIRST

OBSERVATION

33

33

33

33

33

33

-LAST

OBSERVATION

120

120

120

120

120

120

120

120

120

120

120

120

NUMBER

OF

ESTIMATED

PARAMETERS

:

-FIXED

PART

:

.BETAS

77

77

77

77

77

77

.BOX-COX

11

11

11

11

11

11

.ASSOCIATED

DUMMIES

00

00

00

00

00

00

-AUTOCORRELATION

22

22

22

22

22

22

-HETEROSKEDASTICITY

:

.DELTAS

00

00

00

00

00

00

.BOX-COX

00

00

00

00

00

00

.ASSOCIATED

DUMMIES

00

00

00

00

00

00

=================================================================================================================================================

Appendix VII:Analysis of Variance

211

Table 6.9: Analysis of variance: ηPARSER

Effects Sum Sq.a Mean Sq.b Df F test Pr(>F) Percentage Cont.

F 4. 3759 4. 3759 1 7. 19E+05 < 2. 20E-16 99. 822

A 0. 0075 0. 0075 1 1. 23E+03 4. 03E-09 0. 171

DF 0. 0001 0. 0001 1 1. 94E+01 0. 003127 0. 002

CE 0. 0001 0. 0001 1 1. 68E+01 0. 004551 0. 002

E 0. 0001 0. 0001 1 1. 08E+01 0. 013244 0. 002

BF 0 0 1 7. 21E+00 0. 031301

EF 0 0 1 6. 68E+00 0. 036265

BC 0 0 1 5. 20E+00 0. 056643

AD 0 0 1 1. 60E+00 0. 245807

BD 0 0 1 1. 36E+00 0. 282069

ABE 0 0 1 1. 36E+00 0. 282069

BCE 0 0 1 1. 36E+00 0. 282069

BDF 0 0 1 1. 36E+00 0. 282069

CEF 0 0 1 1. 36E+00 0. 282069

ABCE 0 0 1 1. 36E+00 0. 282069

ABCF 0 0 1 1. 36E+00 0. 282069

ACDF 0 0 1 1. 36E+00 0. 282069

AB 0 0 1 1. 13E+00 0. 322666

AC 0 0 1 1. 13E+00 0. 322666

AF 0 0 1 1. 13E+00 0. 322666

CF 0 0 1 1. 13E+00 0. 322666

ABC 0 0 1 1. 13E+00 0. 322666

ABD 0 0 1 1. 13E+00 0. 322666

ADE 0 0 1 1. 13E+00 0. 322666

CDE 0 0 1 1. 13E+00 0. 322666

ADF 0 0 1 1. 13E+00 0. 322666

BCF 0 0 1 1. 13E+00 0. 322666

BEF 0 0 1 1. 13E+00 0. 322666

ADEF 0 0 1 1. 13E+00 0. 322666

ACEF 0 0 1 1. 13E+00 0. 322666

BCDF 0 0 1 1. 13E+00 0. 322666

BCEF 0 0 1 1. 13E+00 0. 322666

AE 0 0 1 9. 27E-01 0. 367799

BE 0 0 1 9. 27E-01 0. 367799

ACD 0 0 1 9. 27E-01 0. 367799

ACE 0 0 1 9. 27E-01 0. 367799

BCD 0 0 1 9. 27E-01 0. 367799

BDE 0 0 1 9. 27E-01 0. 367799

ABF 0 0 1 9. 27E-01 0. 367799

DEF 0 0 1 9. 27E-01 0. 367799

BCDE 0 0 1 9. 27E-01 0. 367799

ABEF 0 0 1 9. 27E-01 0. 367799

BDEF 0 0 1 9. 27E-01 0. 367799

CDEF 0 0 1 9. 27E-01 0. 367799

ABDE 0 0 1 9. 27E-01 0. 367799

D 0 0 1 7. 42E-01 0. 417596

ACF 0 0 1 7. 42E-01 0. 417596

CDF 0 0 1 7. 42E-01 0. 417596

ABCD 0 0 1 7. 42E-01 0. 417596

ABDF 0 0 1 7. 42E-01 0. 417596

DE 0 0 1 5. 78E-01 0. 472086

ACDE 0 0 1 5. 78E-01 0. 472086

CD 0 0 1 4. 34E-01 0. 531184

AEF 0 0 1 4. 34E-01 0. 531184

C 0 0 1 2. 08E-01 0. 662211

B 0 0 1 2. 31E-02 0. 883479

a<0.0001 values are approximated to 0.b<0.0001 values are approximated to 0.

Table 6.10: Analysis of variance: ηCONALC


F 0. 31332 0. 31332 1 16734. 3095 4. 35E-13 94. 543

B 0. 017096 0. 017096 1 913. 0677 1. 12E-08 5. 159

D 0. 00003 0. 00003 1 1. 6156 0. 2443 0. 009

BC 0. 000025 0. 000025 1 1. 3352 0. 2858 0. 008

CDE 0. 000025 0. 000025 1 1. 3352 0. 2858 0. 008

BEF 0. 000025 0. 000025 1 1. 3352 0. 2858 0. 008

AD 0. 000023 0. 000023 1 1. 2051 0. 3086 0. 007

BD 0. 000023 0. 000023 1 1. 2051 0. 3086 0. 007

AF 0. 000023 0. 000023 1 1. 2051 0. 3086 0. 007

BCE 0. 000023 0. 000023 1 1. 2051 0. 3086 0. 007

ADF 0. 000023 0. 000023 1 1. 2051 0. 3086 0. 007

ACDF 0. 000023 0. 000023 1 1. 2051 0. 3086 0. 007

A 0. 00002 0. 00002 1 1. 0815 0. 3329 0. 006

AB 0. 00002 0. 00002 1 1. 0815 0. 3329 0. 006

AC 0. 00002 0. 00002 1 1. 0815 0. 3329 0. 006

AE 0. 00002 0. 00002 1 1. 0815 0. 3329 0. 006

BE 0. 00002 0. 00002 1 1. 0815 0. 3329 0. 006

CF 0. 00002 0. 00002 1 1. 0815 0. 3329 0. 006

ABE 0. 00002 0. 00002 1 1. 0815 0. 3329 0. 006

ACD 0. 00002 0. 00002 1 1. 0815 0. 3329 0. 006

ACE 0. 00002 0. 00002 1 1. 0815 0. 3329 0. 006

ABF 0. 00002 0. 00002 1 1. 0815 0. 3329 0. 006

AEF 0. 00002 0. 00002 1 1. 0815 0. 3329 0. 006

BCF 0. 00002 0. 00002 1 1. 0815 0. 3329 0. 006

CDF 0. 00002 0. 00002 1 1. 0815 0. 3329 0. 006

ABDF 0. 00002 0. 00002 1 1. 0815 0. 3329 0. 006

BCDF 0. 00002 0. 00002 1 1. 0815 0. 3329 0. 006

BCEF 0. 00002 0. 00002 1 1. 0815 0. 3329 0. 006

CDEF 0. 00002 0. 00002 1 1. 0815 0. 3329 0. 006

CD 0. 000018 0. 000018 1 0. 9647 0. 3587 0. 005

BF 0. 000018 0. 000018 1 0. 9647 0. 3587 0. 005

ABD 0. 000018 0. 000018 1 0. 9647 0. 3587 0. 005

ADE 0. 000018 0. 000018 1 0. 9647 0. 3587 0. 005

BDE 0. 000018 0. 000018 1 0. 9647 0. 3587 0. 005

BDF 0. 000018 0. 000018 1 0. 9647 0. 3587 0. 005

CEF 0. 000018 0. 000018 1 0. 9647 0. 3587 0. 005

ABCD 0. 000018 0. 000018 1 0. 9647 0. 3587 0. 005

ACDE 0. 000018 0. 000018 1 0. 9647 0. 3587 0. 005

ABCF 0. 000018 0. 000018 1 0. 9647 0. 3587 0. 005

ABEF 0. 000018 0. 000018 1 0. 9647 0. 3587 0. 005

ACEF 0. 000018 0. 000018 1 0. 9647 0. 3587 0. 005

DE 0. 000016 0. 000016 1 0. 8546 0. 386 0. 005

ABC 0. 000016 0. 000016 1 0. 8546 0. 386 0. 005

BCD 0. 000016 0. 000016 1 0. 8546 0. 386 0. 005

DEF 0. 000016 0. 000016 1 0. 8546 0. 386 0. 005

ABCE 0. 000016 0. 000016 1 0. 8546 0. 386 0. 005

BCDE 0. 000016 0. 000016 1 0. 8546 0. 386 0. 005

ADEF 0. 000016 0. 000016 1 0. 8546 0. 386 0. 005

E 0. 000014 0. 000014 1 0. 7511 0. 4149 0. 004

ACF 0. 000014 0. 000014 1 0. 7511 0. 4149 0. 004

BDEF 0. 000014 0. 000014 1 0. 7511 0. 4149 0. 004

ABDE 0. 000012 0. 000012 1 0. 6543 0. 4452 0. 004

DF 0. 000009 0. 000009 1 0. 4807 0. 5105 0. 003

C 0. 000008 0. 000008 1 0. 4039 0. 5453 0. 002

EF 0. 000005 0. 000005 1 0. 2704 0. 6191 0. 002

CE 0. 000002 0. 000002 1 0. 0835 0. 781 0. 001


Table 6.11: Analysis of variance: ηSUSP


F 0. 099146 0. 099146 1 6345361 < 2. 20E-16 89. 097

C 0. 012018 0. 012018 1 769129 2. 20E-16 10. 800

DF 0. 00007 0. 00007 1 4489 4. 34E-11 0. 063

BF 0. 000021 0. 000021 1 1369 2. 74E-09 0. 019

B 0. 000015 0. 000015 1 961 9. 39E-09 0. 013

D 0. 000003 0. 000003 1 169 3. 71E-06 0. 003

E 0. 000002 0. 000002 1 121 1. 14E-05 0. 002

CE 0. 000001 0. 000001 1 49 0. 0002116 0. 001

DE 0. 000001 0. 000001 1 49 0. 0002116 0. 001

EF 0. 000001 0. 000001 1 49 0. 0002116 0. 001

BEF 0. 000001 0. 000001 1 49 0. 0002116 0. 001

CF 0 0 1 25 0. 0015653

ACF 0 0 1 25 0. 0015653

BCF 0 0 1 25 0. 0015653

BDF 0 0 1 25 0. 0015653

A 0 0 1 9 0. 0199421

AC 0 0 1 9 0. 0199421

BD 0 0 1 9 0. 0199421

BE 0 0 1 9 0. 0199421

ABD 0 0 1 9 0. 0199421

ACD 0 0 1 9 0. 0199421

BDE 0 0 1 9 0. 0199421

ADF 0 0 1 9 0. 0199421

CEF 0 0 1 9 0. 0199421

ABCD 0 0 1 9 0. 0199421

BCDE 0 0 1 9 0. 0199421

ACDF 0 0 1 9 0. 0199421

BCDF 0 0 1 9 0. 0199421

CDEF 0 0 1 9 0. 0199421

ABDE 0 0 1 9 0. 0199421

AB 0 0 1 1 0. 3506167

AD 0 0 1 1 0. 3506167

AE 0 0 1 1 0. 3506167

BC 0 0 1 1 0. 3506167

CD 0 0 1 1 0. 3506167

AF 0 0 1 1 0. 3506167

ABC 0 0 1 1 0. 3506167

ABE 0 0 1 1 0. 3506167

ADE 0 0 1 1 0. 3506167

ACE 0 0 1 1 0. 3506167

BCD 0 0 1 1 0. 3506167

BCE 0 0 1 1 0. 3506167

CDE 0 0 1 1 0. 3506167

ABF 0 0 1 1 0. 3506167

AEF 0 0 1 1 0. 3506167

CDF 0 0 1 1 0. 3506167

DEF 0 0 1 1 0. 3506167

ABCE 0 0 1 1 0. 3506167

ACDE 0 0 1 1 0. 3506167

ABCF 0 0 1 1 0. 3506167

ABDF 0 0 1 1 0. 3506167

ABEF 0 0 1 1 0. 3506167

ADEF 0 0 1 1 0. 3506167

ACEF 0 0 1 1 0. 3506167

BCEF 0 0 1 1 0. 3506167

BDEF 0 0 1 1 0. 3506167


Table 6.12: Analysis of variance: ηDLAB


D 0. 49386 0. 49386 1 2. 13E+06 < 2. 20E-16 97. 251

F 0. 01363 0. 01363 1 5. 87E+04 5. 38E-15 2. 684

DF 0. 00011 0. 00011 1 4. 75E+02 1. 08E-07 0. 022

C 0. 00009 0. 00009 1 3. 69E+02 2. 59E-07 0. 018

B 0. 00006 0. 00006 1 2. 42E+02 1. 09E-06 0. 012

EF 0. 00004 0. 00004 1 1. 82E+02 2. 89E-06 0. 008

CE 0. 00002 0. 00002 1 9. 72E+01 2. 35E-05 0. 004

BF 0. 00001 0. 00001 1 2. 69E+01 0. 001269 0. 002

E 0 0 1 1. 32E+01 0. 008374

ADF 0 0 1 9. 69E+00 0. 017004

CDEF 0 0 1 6. 73E+00 0. 035717

AC 0 0 1 4. 31E+00 0. 076593

BC 0 0 1 4. 31E+00 0. 076593

CF 0 0 1 4. 31E+00 0. 076593

AEF 0 0 1 4. 31E+00 0. 076593

ABDE 0 0 1 4. 31E+00 0. 076593

AB 0 0 1 2. 42E+00 0. 163515

BE 0 0 1 2. 42E+00 0. 163515

ACE 0 0 1 2. 42E+00 0. 163515

CDE 0 0 1 2. 42E+00 0. 163515

BEF 0 0 1 2. 42E+00 0. 163515

CEF 0 0 1 2. 42E+00 0. 163515

DEF 0 0 1 2. 42E+00 0. 163515

ABCD 0 0 1 2. 42E+00 0. 163515

BCDE 0 0 1 2. 42E+00 0. 163515

ACDE 0 0 1 2. 42E+00 0. 163515

ABCF 0 0 1 2. 42E+00 0. 163515

BCEF 0 0 1 2. 42E+00 0. 163515

AD 0 0 1 1. 08E+00 0. 333899

AE 0 0 1 1. 08E+00 0. 333899

DE 0 0 1 1. 08E+00 0. 333899

AF 0 0 1 1. 08E+00 0. 333899

ABD 0 0 1 1. 08E+00 0. 333899

ABE 0 0 1 1. 08E+00 0. 333899

ABF 0 0 1 1. 08E+00 0. 333899

ACF 0 0 1 1. 08E+00 0. 333899

BCF 0 0 1 1. 08E+00 0. 333899

BDF 0 0 1 1. 08E+00 0. 333899

ABEF 0 0 1 1. 08E+00 0. 333899

ACDF 0 0 1 1. 08E+00 0. 333899

ADEF 0 0 1 1. 08E+00 0. 333899

ACEF 0 0 1 1. 08E+00 0. 333899

A 0 0 1 2. 69E-01 0. 619844

BD 0 0 1 2. 69E-01 0. 619844

CD 0 0 1 2. 69E-01 0. 619844

ADE 0 0 1 2. 69E-01 0. 619844

BCD 0 0 1 2. 69E-01 0. 619844

BCE 0 0 1 2. 69E-01 0. 619844

BDE 0 0 1 2. 69E-01 0. 619844

CDF 0 0 1 2. 69E-01 0. 619844

ABCE 0 0 1 2. 69E-01 0. 619844

ABDF 0 0 1 2. 69E-01 0. 619844

BCDF 0 0 1 2. 69E-01 0. 619844

BDEF 0 0 1 2. 69E-01 0. 619844

ABC 0 0 1 0. 00E+00 1

ACD 0 0 1 0. 00E+00 1


Table 6.13: Analysis of variance: ηCOMTOT


F 1. 88582 1. 88582 1 19405. 6728 2. 59E-13 94. 331

E 0. 10709 0. 10709 1 1102. 0183 5. 83E-09 5. 357

CE 0. 00052 0. 00052 1 5. 3259 0. 05436 0. 026

B 0. 00036 0. 00036 1 3. 7148 0. 09529 0. 018

C 0. 00033 0. 00033 1 3. 4273 0. 10656 0. 017

EF 0. 00026 0. 00026 1 2. 6343 0. 14861 0. 013

BF 0. 00017 0. 00017 1 1. 7391 0. 22876 0. 009

BCF 0. 00012 0. 00012 1 1. 1892 0. 3116 0. 006

AF 0. 00011 0. 00011 1 1. 1345 0. 32217 0. 006

ACF 0. 00011 0. 00011 1 1. 1345 0. 32217 0. 006

AD 0. 00011 0. 00011 1 1. 0811 0. 33302 0. 006

BD 0. 00011 0. 00011 1 1. 0811 0. 33302 0. 006

DE 0. 00011 0. 00011 1 1. 0811 0. 33302 0. 006

ABF 0. 00011 0. 00011 1 1. 0811 0. 33302 0. 006

AC 0. 0001 0. 0001 1 1. 029 0. 34416 0. 005

BE 0. 0001 0. 0001 1 1. 029 0. 34416 0. 005

ABC 0. 0001 0. 0001 1 1. 029 0. 34416 0. 005

ACD 0. 0001 0. 0001 1 1. 029 0. 34416 0. 005

ADE 0. 0001 0. 0001 1 1. 029 0. 34416 0. 005

CDF 0. 0001 0. 0001 1 1. 029 0. 34416 0. 005

ABCD 0. 0001 0. 0001 1 1. 029 0. 34416 0. 005

ABCF 0. 0001 0. 0001 1 1. 029 0. 34416 0. 005

ADEF 0. 0001 0. 0001 1 1. 029 0. 34416 0. 005

BCEF 0. 0001 0. 0001 1 1. 029 0. 34416 0. 005

CDEF 0. 0001 0. 0001 1 1. 029 0. 34416 0. 005

CD 0. 0001 0. 0001 1 0. 9782 0. 35558 0. 005

ACE 0. 0001 0. 0001 1 0. 9782 0. 35558 0. 005

BCD 0. 0001 0. 0001 1 0. 9782 0. 35558 0. 005

CDE 0. 0001 0. 0001 1 0. 9782 0. 35558 0. 005

AEF 0. 0001 0. 0001 1 0. 9782 0. 35558 0. 005

CEF 0. 0001 0. 0001 1 0. 9782 0. 35558 0. 005

ABCE 0. 0001 0. 0001 1 0. 9782 0. 35558 0. 005

BCDE 0. 0001 0. 0001 1 0. 9782 0. 35558 0. 005

ABDF 0. 0001 0. 0001 1 0. 9782 0. 35558 0. 005

ABEF 0. 0001 0. 0001 1 0. 9782 0. 35558 0. 005

ACDF 0. 0001 0. 0001 1 0. 9782 0. 35558 0. 005

ACEF 0. 0001 0. 0001 1 0. 9782 0. 35558 0. 005

BDEF 0. 0001 0. 0001 1 0. 9782 0. 35558 0. 005

ABDE 0. 0001 0. 0001 1 0. 9782 0. 35558 0. 005

AE 0. 00009 0. 00009 1 0. 9287 0. 3673 0. 005

ABE 0. 00009 0. 00009 1 0. 9287 0. 3673 0. 005

BCE 0. 00009 0. 00009 1 0. 9287 0. 3673 0. 005

BEF 0. 00009 0. 00009 1 0. 9287 0. 3673 0. 005

ACDE 0. 00009 0. 00009 1 0. 9287 0. 3673 0. 005

BCDF 0. 00009 0. 00009 1 0. 9287 0. 3673 0. 005

AB 0. 00009 0. 00009 1 0. 8805 0. 37931 0. 005

ABD 0. 00009 0. 00009 1 0. 8805 0. 37931 0. 005

BDE 0. 00008 0. 00008 1 0. 8335 0. 39162 0. 004

ADF 0. 00008 0. 00008 1 0. 8335 0. 39162 0. 004

BDF 0. 00008 0. 00008 1 0. 8335 0. 39162 0. 004

DEF 0. 00008 0. 00008 1 0. 8335 0. 39162 0. 004

CF 0. 00008 0. 00008 1 0. 7879 0. 40421 0. 004

DF 0. 00008 0. 00008 1 0. 7879 0. 40421 0. 004

A 0. 00007 0. 00007 1 0. 7004 0. 43029 0. 004

BC 0. 00005 0. 00005 1 0. 5042 0. 50061 0. 003

D 0 0 1 0. 0412 0. 845


Table 6.14: Analysis of variance: ρ1


F 0. 34325 0. 34325 1 1. 03E+07 < 2. 20E-16 99. 997

DF 0. 00001 0. 00001 1 2. 06E+02 1. 90E-06 0. 003

C 0 0 1 7. 89E+01 4. 65E-05

BF 0 0 1 5. 65E+01 0. 0001356

E 0 0 1 3. 78E+01 0. 0004684

B 0 0 1 2. 29E+01 0. 0020078

BE 0 0 1 2. 29E+01 0. 0020078

CE 0 0 1 2. 29E+01 0. 0020078

EF 0 0 1 2. 29E+01 0. 0020078

BCF 0 0 1 2. 29E+01 0. 0020078

AE 0 0 1 1. 17E+01 0. 0112014

BC 0 0 1 1. 17E+01 0. 0112014

AF 0 0 1 1. 17E+01 0. 0112014

DEF 0 0 1 1. 17E+01 0. 0112014

ABEF 0 0 1 1. 17E+01 0. 0112014

ACDF 0 0 1 1. 17E+01 0. 0112014

A 0 0 1 4. 20E+00 0. 079602

D 0 0 1 4. 20E+00 0. 079602

CF 0 0 1 4. 20E+00 0. 079602

ADE 0 0 1 4. 20E+00 0. 079602

CDE 0 0 1 4. 20E+00 0. 079602

CEF 0 0 1 4. 20E+00 0. 079602

AB 0 0 1 4. 67E-01 0. 5164896

AC 0 0 1 4. 67E-01 0. 5164896

AD 0 0 1 4. 67E-01 0. 5164896

BD 0 0 1 4. 67E-01 0. 5164896

CD 0 0 1 4. 67E-01 0. 5164896

DE 0 0 1 4. 67E-01 0. 5164896

ABC 0 0 1 4. 67E-01 0. 5164896

ABD 0 0 1 4. 67E-01 0. 5164896

ABE 0 0 1 4. 67E-01 0. 5164896

ACD 0 0 1 4. 67E-01 0. 5164896

ACE 0 0 1 4. 67E-01 0. 5164896

BCD 0 0 1 4. 67E-01 0. 5164896

BCE 0 0 1 4. 67E-01 0. 5164896

BDE 0 0 1 4. 67E-01 0. 5164896

ABF 0 0 1 4. 67E-01 0. 5164896

ACF 0 0 1 4. 67E-01 0. 5164896

ADF 0 0 1 4. 67E-01 0. 5164896

AEF 0 0 1 4. 67E-01 0. 5164896

BDF 0 0 1 4. 67E-01 0. 5164896

BEF 0 0 1 4. 67E-01 0. 5164896

CDF 0 0 1 4. 67E-01 0. 5164896

ABCD 0 0 1 4. 67E-01 0. 5164896

ABCE 0 0 1 4. 67E-01 0. 5164896

BCDE 0 0 1 4. 67E-01 0. 5164896

ACDE 0 0 1 4. 67E-01 0. 5164896

ABCF 0 0 1 4. 67E-01 0. 5164896

ABDF 0 0 1 4. 67E-01 0. 5164896

ADEF 0 0 1 4. 67E-01 0. 5164896

ACEF 0 0 1 4. 67E-01 0. 5164896

BCDF 0 0 1 4. 67E-01 0. 5164896

BCEF 0 0 1 4. 67E-01 0. 5164896

BDEF 0 0 1 4. 67E-01 0. 5164896

CDEF 0 0 1 4. 67E-01 0. 5164896

ABDE 0 0 1 4. 67E-01 0. 5164896


Table 6.15: Analysis of variance: ρ2


F 0. 103765 0. 103765 1 6. 55E+05 < 2. 20E-16 99. 897

CE 0. 000032 0. 000032 1 2. 00E+02 2. 11E-06 0. 031

D 0. 000017 0. 000017 1 1. 07E+02 1. 69E-05 0. 016

B 0. 000015 0. 000015 1 9. 47E+01 2. 56E-05 0. 014

C 0. 000013 0. 000013 1 8. 29E+01 3. 95E-05 0. 013

DF 0. 000011 0. 000011 1 7. 19E+01 6. 28E-05 0. 011

BF 0. 000008 0. 000008 1 5. 22E+01 0. 0001741 0. 008

E 0. 000006 0. 000006 1 3. 56E+01 0. 0005611 0. 006

BC 0. 000002 0. 000002 1 1. 19E+01 0. 0106347 0. 002

A 0. 000001 0. 000001 1 7. 99E+00 0. 0255547 0. 001

BDF 0. 000001 0. 000001 1 4. 83E+00 0. 0639241 0. 001

ABCE 0. 000001 0. 000001 1 4. 83E+00 0. 0639241 0. 001

ACF 0 0 1 2. 46E+00 0. 1604145

CDF 0 0 1 2. 46E+00 0. 1604145

CDEF 0 0 1 2. 46E+00 0. 1604145

AB 0 0 1 8. 87E-01 0. 3775675

AD 0 0 1 8. 87E-01 0. 3775675

BE 0 0 1 8. 87E-01 0. 3775675

CD 0 0 1 8. 87E-01 0. 3775675

AF 0 0 1 8. 87E-01 0. 3775675

ABC 0 0 1 8. 87E-01 0. 3775675

ADE 0 0 1 8. 87E-01 0. 3775675

BCD 0 0 1 8. 87E-01 0. 3775675

BCE 0 0 1 8. 87E-01 0. 3775675

CDE 0 0 1 8. 87E-01 0. 3775675

ABF 0 0 1 8. 87E-01 0. 3775675

ADF 0 0 1 8. 87E-01 0. 3775675

DEF 0 0 1 8. 87E-01 0. 3775675

ACDE 0 0 1 8. 87E-01 0. 3775675

ABCF 0 0 1 8. 87E-01 0. 3775675

ABDF 0 0 1 8. 87E-01 0. 3775675

ABEF 0 0 1 8. 87E-01 0. 3775675

ADEF 0 0 1 8. 87E-01 0. 3775675

ABDE 0 0 1 8. 87E-01 0. 3775675

AC 0 0 1 9. 86E-02 0. 7626771

AE 0 0 1 9. 86E-02 0. 7626771

BD 0 0 1 9. 86E-02 0. 7626771

DE 0 0 1 9. 86E-02 0. 7626771

CF 0 0 1 9. 86E-02 0. 7626771

EF 0 0 1 9. 86E-02 0. 7626771

ABD 0 0 1 9. 86E-02 0. 7626771

ABE 0 0 1 9. 86E-02 0. 7626771

ACD 0 0 1 9. 86E-02 0. 7626771

ACE 0 0 1 9. 86E-02 0. 7626771

BDE 0 0 1 9. 86E-02 0. 7626771

AEF 0 0 1 9. 86E-02 0. 7626771

BCF 0 0 1 9. 86E-02 0. 7626771

BEF 0 0 1 9. 86E-02 0. 7626771

CEF 0 0 1 9. 86E-02 0. 7626771

ABCD 0 0 1 9. 86E-02 0. 7626771

BCDE 0 0 1 9. 86E-02 0. 7626771

ACDF 0 0 1 9. 86E-02 0. 7626771

ACEF 0 0 1 9. 86E-02 0. 7626771

BCDF 0 0 1 9. 86E-02 0. 7626771

BCEF 0 0 1 9. 86E-02 0. 7626771

BDEF 0 0 1 9. 86E-02 0. 7626771


Table 6.16: Analysis of variance: λ


F 3. 7893 3. 7893 1 3. 25E+05 < 2. 20E-16 99. 491

CE 0. 011 0. 011 1 9. 42E+02 1. 01E-08 0. 289

DF 0. 0042 0. 0042 1 3. 60E+02 2. 80E-07 0. 110

C 0. 0017 0. 0017 1 1. 48E+02 5. 75E-06 0. 045

B 0. 0011 0. 0011 1 9. 40E+01 2. 63E-05 0. 029

D 0. 0006 0. 0006 1 5. 19E+01 0. 0001765 0. 016

BC 0. 0003 0. 0003 1 2. 30E+01 0. 0019843 0. 008

EF 0. 0002 0. 0002 1 1. 96E+01 0. 0030579 0. 005

E 0. 0002 0. 0002 1 1. 65E+01 0. 0048065 0. 005

BF 0. 0001 0. 0001 1 1. 01E+01 0. 0154357 0. 003

CD 0 0 1 3. 76E+00 0. 0937007

ACD 0 0 1 3. 21E+00 0. 1161567

BE 0 0 1 2. 47E+00 0. 1597197

DE 0 0 1 2. 47E+00 0. 1597197

A 0 0 1 1. 83E+00 0. 2179717

DEF 0 0 1 1. 64E+00 0. 2412173

CDE 0 0 1 1. 46E+00 0. 2665681

AD 0 0 1 1. 29E+00 0. 2941266

AEF 0 0 1 1. 29E+00 0. 2941266

ACEF 0 0 1 1. 29E+00 0. 2941266

AF 0 0 1 1. 13E+00 0. 3239822

ABC 0 0 1 1. 13E+00 0. 3239822

ABE 0 0 1 1. 13E+00 0. 3239822

BCD 0 0 1 1. 13E+00 0. 3239822

ADF 0 0 1 1. 13E+00 0. 3239822

ABCE 0 0 1 1. 13E+00 0. 3239822

ABDF 0 0 1 1. 13E+00 0. 3239822

ADEF 0 0 1 1. 13E+00 0. 3239822

BDEF 0 0 1 1. 13E+00 0. 3239822

ADE 0 0 1 9. 76E-01 0. 3562073

BCE 0 0 1 9. 76E-01 0. 3562073

ABF 0 0 1 9. 76E-01 0. 3562073

BEF 0 0 1 9. 76E-01 0. 3562073

CDF 0 0 1 9. 76E-01 0. 3562073

ABCD 0 0 1 9. 76E-01 0. 3562073

ACDE 0 0 1 9. 76E-01 0. 3562073

ABCF 0 0 1 9. 76E-01 0. 3562073

ABEF 0 0 1 9. 76E-01 0. 3562073

ACDF 0 0 1 9. 76E-01 0. 3562073

BCDF 0 0 1 9. 76E-01 0. 3562073

BCEF 0 0 1 9. 76E-01 0. 3562073

CDEF 0 0 1 9. 76E-01 0. 3562073

ABDE 0 0 1 9. 76E-01 0. 3562073

AC 0 0 1 8. 36E-01 0. 3908532

AE 0 0 1 8. 36E-01 0. 3908532

ACE 0 0 1 8. 36E-01 0. 3908532

ACF 0 0 1 8. 36E-01 0. 3908532

CEF 0 0 1 8. 36E-01 0. 3908532

BCDE 0 0 1 8. 36E-01 0. 3908532

ABD 0 0 1 7. 08E-01 0. 4279468

BDE 0 0 1 4. 83E-01 0. 5094361

AB 0 0 1 3. 87E-01 0. 5537283

BD 0 0 1 1. 08E-01 0. 7516136

BCF 0 0 1 1. 08E-01 0. 7516136

CF 0 0 1 6. 56E-02 0. 8052607

BDF 0 0 1 3. 35E-02 0. 860057


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