A New Econometric Approach for Modeling Several Count Variables : A Case Study of Crash Frequency Analysis by Crash Type and Severity

There is limited adoption of research modeling crash severity frequency considering different crash types due to the challenge associated with analyzing large number of dependent variables. The proposed research contributes to burgeoning econometric and safety literature by developing a joint modeling approach that can accommodate for several dependent variables within a parsimonious structure. By recasting the analysis levels for dependent variables, the proposed approach allows for flexible consideration of crashes by type and severity within a single framework. Specifically, we employ a Panel Mixed Negative Binomial- Generalized Ordered Probit Fractional Spilt (PMNB-GOPFS) model where the first component (NB) accommodates for crash frequency by crash type and the later component (GOPFS) studies the fraction of severity outcome for different crash types. The proposed model system increases interaction between dependent variables through observed variables thus reducing the dependency on unobserved interactions across dependent variables. Thus, the proposed approach allows for the estimation of parsimonious specifications reducing the need for computationally intensive simulation based estimation. The proposed system is also flexible to accommodate for common unobserved effects including: 1) common unobserved factors simultaneously affecting crash counts of different crash types; 2) common unobserved factors simultaneously affecting crash severity proportions of different crash types; and 3) common unobserved factors that simultaneously impact crash counts and severity proportions by different crash types. The model system performance is illustrated using a simulation study. The empirical analysis was conducted using zonal level crash count data for the year 2016 from Central Florida while considering a comprehensive set of exogenous variables including roadway, built environment, land-use, traffic and sociodemographic characteristics. To illustrate the applicability of our proposed system, we carried out a comparison exercise between our proposed joint PMNB-GOPFS and the traditional multivariate system for predicting crash counts across different crash severities. The resulting goodness of fit measures clearly highlight the superior/equivalent performance of the proposed PMNB-GOPFS model over the traditional RPMNB model with less than half the number of parameters. The proposed framework can predict several dimensions including total crash counts, total crash counts by crash types, crash counts for each severity level and finally, proportions and counts of crashes for each crash type by severity.