Grouped Random Parameters Negative Binomial-Lindley for accounting unobserved heterogeneity in crash data with preponderant zero observations

Abstract

Developing robust and reliable statistical models to estimate, analyze, and understand crash data is a key element in various highway safety evaluation tasks. Crash data have characteristics not found in other data, including but not limited to the excess number of zero responses. The Negative Binomial-Lindley (NB-L) model has been proposed as a method to analyze data with many zero observations. In addition, the differences in various temporal and spatial factors result in variations of model coefficients among different groups of observations. A grouped random parameters model is a strategy to account for such unobserved heterogeneity. In this paper, we proposed the derivations and applications of the grouped random parameters negative binomial-Lindley model (G-RPNB-L) to account for the unobserved heterogeneity in crash data with many zero observations. We first illustrated our proposed model by designing a simulation study. The simulation study showed the ability of the proposed model to correctly estimate the coefficients. Then, we used an empirical dataset in Maine to show the application of the proposed model. We showed that the impact of weather variables denoting “Days with precipitation greater than 1.0 in.”, and “Days with temperature less than 32°F” varies across Maine counties. We also compared the proposed model with the NB, NB-L, and grouped random-parameters NB (G-RPNB) models using different goodness-of-fit metrics. The proposed G-RPNB-L model showed a superior fit compared to the other models.