The effect of variations in spatial units on unobserved heterogeneity in macroscopic crash models

Macroscopic safety models establish a relationship between crashes and the contributing factors in a defined spatial unit. Negative binomial (NB) and Bayesian negative binomial models with conditional autoregressive prior (CAR) are techniques widely used to establish this relationship. However, these models do not account for unobserved heterogeneity and their output is global and fixed irrespective of the spatial unit of the analysis. There is a timely need to understand how variations in spatial units affect unobserved heterogeneity. This study uses two advanced modeling techniques, the random parameter negative binomial (RPNB) and the semi-parametric geographically weighted Poisson regression (S-GWPR), to investigate whether explanatory variables found to be significant and random in one spatial aggregation will remain significant and random when another spatial aggregation is used. The key finding is that variations in spatial units do have an impact on unobserved heterogeneity. We also found that variations in spatial units have a greater impact on unobserved heterogeneity in the RPNB models compared to the S-GWPR models. We found that the S-GWPR model performs better than the RPNB model with the lowest value of mean absolute deviation (MAD) and Akaiki information criterion (AIC) but the two modeling techniques produce similar results in terms of the sign of the coefficients across the selected spatial units of analysis. Overall, the study provides a methodological basis for assessing the impact of spatial units on unobserved heterogeneity.