Correlated Random Parameter Marginalized Two-Part Model: Application to Refined-Scale Longitudinal Crash Rates Data

Abstract

Crash rate data are mainly analyzed using the Tobit model. However, there are three major limitations associated with the Tobit model when it is applied to crash data: (1) the assumption that zeros are originated from the data generating process, (2) the presumption of a normal distribution of the latent response variable, and (3) the Tobit proportionality assumption. Moreover, unobserved heterogeneities are usually present, which lead to biased results in crash analyses. To address these limitations, the marginalized two-part model with random parameter specification is proposed as an alternative to the Tobit model. For comparison purposes, four models are developed: (1) Tobit model, (2) fixed parameter marginalized two-part (FPMTP) model, (3) uncorrelated random parameter marginalized two-part (URPMTP) model, and (4) correlated random parameter marginalized two-part (CRPMTP) model. The proposed methodology is demonstrated by investigating daily crash rates on a major freeway in Colorado. Model estimation results show that marginalized two-part models outperform the Tobit model, exhibiting good potential for future adoption when studying crash rates. Among the three two-part models, CRPMTP outperforms the other two, indicating that the correlated random parameter model can better capture the unobserved heterogeneities. Furthermore, the time-varying variables, including traffic and weather variables, are also found to play a significant role in crash occurrence.