Finite mixture Negative Binomial-Lindley for modeling heterogeneous crash data with many zero observations

Crash data are often highly dispersed; it may also include a large amount of zero observations or have a long tail. The traditional Negative Binomial (NB) model cannot model these data properly. To overcome this issue, the Negative Binomial-Lindley (NB-L) model has been proposed as an alternative to the NB to analyze data with these characteristics. Research studies have shown that the NB-L model provides a superior performance compared to the NB when data include numerous zero observations or have a long tail. In addition, crash data are often collected from sites with different spatial or temporal characteristics. Therefore, it is not unusual to assume that crash data are drawn from multiple subpopulations. Finite mixture models are powerful tools that can be used to account for underlying subpopulations and capture the population heterogeneity. This research documents the derivations and characteristics of the Finite mixture NB-L model (FMNB-L) to analyze data generated from heterogeneous subpopulations with many zero observations and a long tail. We demonstrated the application of the model to identify subpopulations with a simulation study. We then used the FMNB-L model to estimate statistical models for Texas four-lane freeway crashes. These data have unique characteristics; it is highly dispersed, have many locations with very large number of crashes, as well as significant number of locations with zero crash. We used multiple goodness-of-fit metrics to compare the FMNB-L model with the NB, NB-L, and the finite mixture NB models. The FMNB-L identified two subpopulations in datasets. The results show a significantly better fit by the FMNB-L compared to other analyzed models.