Modeling unobserved heterogeneity using finite mixture random parameters for spatially correlated discrete count data

• Road segments tend to group in terms of the influence of road features on the respective road safety due to unknown reasons.
• Finite-mixture specifications facilitate to investigate the underlying groups of road segments, while allowing for within group heterogeneity.
• A negative binomial specification with finite-mixture distributed random parameters that simultaneously accounts for potential spatial correlation was developed.
• A Gibbs sampling framework is proposed that leverages recent theoretical developments on data-augmentation algorithms, and elegantly sidesteps many of the computational difficulties usually associated with Bayesian inference of count models.
• Empirical results suggested that the influence of road condition was uniform across the latent groups of road segments, while the influence of shoulder width was significantly different.

Road segments with identical site-specific attributes often exhibit significantly different crash counts due to unobserved reasons. The extent of unobserved heterogeneity associated with a road feature is to be estimated prior to selecting the relevant safety treatment. Moreover, crash count data is often over-dispersed and spatially correlated. This paper proposes a spatial negative binomial specification with random parameters for modeling crash counts of contiguous road segments. The unobserved heterogeneity is incorporated using a finite multi-variate normal mixture prior on the random parameters; this allows for non-normality, skewness in the distribution of the random parameters, facilitates correlation across the random parameters, and relaxes any distributional assumptions. The model extracts the inherent groups of road segments with crash counts that are equally sensitive to the road attributes on an average; the heterogeneity within these groups is also allowed in the proposed framework. The specification simultaneously accounts for potential spatial correlation of the crash counts from neighboring road segments. A Gibbs sampling framework is proposed that leverages recent theoretical developments on data-augmentation algorithms, and elegantly sidesteps many of the computational difficulties usually associated with Bayesian inference of count models. Empirical results suggests the presence of two latent groups and spatial correlation within the study road network. Road features with significantly different effect on crash counts across two latent groups of road segments were identified.