Random Parameters Model For Freeway Traffic Crash Considering Heterogeneity And Endogeneity

Traffic crashes annually result in enormous death,injuries and property lost,and road traffic safety is drawing increasing attentions from all circles of the society.Identifing crash rules through deep analysis of crash data so as to provide decision basis for developing countermeasures is the most straightforward and effective way to improve traffic safety.Howerver,a reliable analyzing and modeling method is the foundation and precondition of that.The analytical accuracy can be improved and more valuable traffic safety information can be extracted from the limited modeling data through advancing and optimizing traditional models,i.e.,traffic safety level can be ultimately improved by optimizing current exsiting methods.This has been one of the most important directions for traffic safety analytical methodologies,thus poessess continuous research potential and vast application prospect.Heterogeneity and endogeneity of modeling data are the most fundamental factors affecting model's reliability,which are also factors prone to be ignored during modeling.The improvement of traditional fixed parameters model and the application of improved model to freeway safety analysis were investigated in this study from the perspective of controlling heterogeneity and endogeneity.Firstly,literatures at home and abroad relating to crash frequency models,heterogeneity and endogeneity and crash factors were reviewed,and applications of count models to road traffic safety were particularly analyzed.The existing research achievements were summarized,and advantages and problems of currently used models were analyzed.Based on that,effects of heterogeneity and endogeneity on model's reliability were investigated,and then directions for model improvement and methods for model optimization were proposed.Secondly,combined with data of crash,traffic operating,road design and weather conditons from eight Chinese freeways,the reasonable range of road segment length was determined by the crash integration function following the process of road segmentation.Then,sample outliers were identified by Cook distance and the treatment method for outliers was presented.The multicollinearity and autocorrelation were subsequently detected by the three indexes of Pearson Correlation Coefficient,Cramer 's V and Introclass Correlation Coefficient.Thirdly,the Possion process for crash was then clarified from aspects of the generating process and the statistical distribution of crashes.Considerating the overdisperson characteristics of crash data,a negative binomial(NB)model was developed.For observations with preponderant zero,principles of zero inflated Possion(ZIP)and zero inflated negative binomial(ZINB)models were presented.The distribution of crash frequency was finally determined after a comprehensive evaluation of crash generating process,model goodness-of-fit(GOF)and prediction accuracy.Fourthly,due to the incapability of traditional fixed parameters model on reflecting heterogeneity,a model improving method by randomizing parameters was proposed.Considering the fact that the overdisperson parameter varies across sample groups,a random effects negative binomial(RENB)model was constructed.Based on the assumption that effects of crash contributing factors on safety are not constant across all observations,a random parameters negative binomial(RPNB)model with varying parameters for independent variables was developed.Then,estimating methods for parameters were presented,and the preferred one between the two models was selected out.To further investigate the interactive effects of heterogenous factors on crash,a correlated random parameters negative binomial(CRPNB)model was then developed by transforming the diagonal coefficient matrix of random terms to an unrestricted matrix with free potential values for each matrix element.Meanwhile,a GOF evaluating method for the CRPNB model based on distribution of cumulative residuals was presented.Finally,after integrating the heterogeneity,a method for controlling endogeneity through sample matching was further proposed.The matching principle and process based on propensity scores were put forward,and the constructing procedure for the propensity score model was then presented.The propensity score based matching algorithms that are nearest neighbor matching,Mahalanobis matching and genetic matching were also exhibited.The CRPNB model using matched samples was calibrated to decrease the adverse effects of heterogeneity on modeling.The proposed RPNB model,CRPNB model and CRPNB model based on matched samples were applied to safety analysis for freeway basic segments,tunnel segments and climbing segments,respectively.Results indicated that crash frequency follows a NB distribution.More cautions should be paid when using ZIP and ZINB models as they cannot fully reflect the logic generating process of crash.The RENB and RPNB models can both reflect heterogeneity,while the RPNB model outperformed the RENB model from the point of view of GOF.The CRPNB model can further reflect correlations among heterogeneities,thus indicating an improved GOF and producing more safety related conclusions.The CRPNB model using propensity score based matching samples could simultaneously control the adverse effects of heterogeneity and endogeneity on modeling reliability.Based on proposed models,a total number of 28 factors significantly affecting freeway crashes were identified.A total number of 12 factors significantly affecting tunnel safety were also identified,and their interactive effects on tunnel safety were revealed.Inferences of installing climbing lanes could mitigate the adverse effects of proportion of heavy vehicles and distance along composite ascending grade on safety,and consequently decrease the crash rate by about 17 percent were concluded.Results from this study demonstrated the feasibility and effectiveness of controlling heterogeneity and endogeneity by random parameters models,thus can provide new sights and methods for improving traditional models and supplement the current methodological theory of crash analysis.On the other hand,the proposed models can be applied to practical safety analysis of roads and be beneficial to develop more specific safety coutnermeasures and improve the safety level of road design,management and operation.