A Poisson Lognormal-Lindley model for simultaneous estimation of multiple crash-types: Application of multivariate and pooled univariate models

Challenges addressing overdispersion, unobserved heterogeneity, the preponderance of zeros, and correlation in the dependent variables of crash count models are of significant interest. Accounting for all these data issues simultaneously is few and far between. This study proposes a new mixing distribution model that accounts for overdispersion and the preponderance of zeros in crash count models. The proposed mixing distribution model extends to the multivariate structure to account for correlations between dependent variables and unobserved heterogeneity. The empirical analysis is conducted on crash data of Bruce highway involving single-vehicle and multi-vehicle crash types by "fatal and severe injury" and "moderate and minor injury" severity levels on aggregated data over three analysis years (2016, 2017, and 2018). The study demonstrates superior goodness of fit of the proposed multivariate random parameters Poisson lognormal-Lindley model compared to its restricted models. Moreover, pooling the crash data as repeated measures of crash types helped formulate a pooled-univariate random parameters Poisson-Lindley model to estimate multiple crash types by severity. The results showed the pooled-univariate model offers comparable goodness of fit and averaged marginal effects as the complex multivariate modeling structure. Moreover, the proposed pooled-univariate model reduced the model complexity to a one-dimensional integral and offered more efficient parameter estimates. In the empirical context, the modeling results showed that single-vehicle and multi vehicle crashes by severity are linked with different causality.