The negative binomial Lindley model with spatiotemporal random parameters: accounting for spatiotemporal effects in crash data analysis

The standard negative binomial (NB) and negative binomial-Lindley (NBL) models may not completely capture variations associated with time and space. To address these limitations, this study derives an enhanced version of the NBL model that simultaneously incorporates spatiotemporal random parameters to account for three key factors: temporal variations, spatial variations, and datasets with a large amount of zero observations. The proposed framework extends the standard NBL model by allowing both model coefficients and Lindley parameters to vary over time and across space together. This approach captures the heterogeneity in crash data caused by variations in spatiotemporal factors associated with traffic patterns, environmental conditions, or geographic differences, while also addressing the high proportion of zero observations typically found in such datasets. The results demonstrate that the proposed model reasonably recovers the true parameters. Findings indicate that the proposed model outperforms those that solely account for temporal or spatial variations.