Bayesian Spatial-temporal Modeling of Deer–Vehicle Collisions on State Roads: A Segment-Level Analysis in Pennsylvania

Deer–vehicle collisions (DVCs) are a persistent safety and economic concern in Pennsylvania, yet quantitative tools for identifying high-risk locations at the road-segment scale remain limited. This study develops a Bayesian spatiotemporal modeling framework for DVCs on state-maintained roads, using PennDOT Public Crash Data linked to the State Road Segment (RMSSEG) inventory. Police- and driver-reported crashes from 2018–2024 were geocoded and matched to homogeneous state road segments, then aggregated to segment–quarter counts. Segment-level covariates included total paved width, lane count, an ordinal urban–rural classification, and annual average daily traffic (AADT), which entered the model as an exposure offset. Exploratory analysis showed that DVCs are rare and highly zero-inflated at the segment–quarter level, exhibit a stable seasonal pattern with peaks in the fourth quarter, and increase monotonically with traffic volume. We modeled DVC counts using negative binomial (NB) mixed-effects models with a shared log-linear predictor incorporating BYM2 spatial random components, a first-order temporal random walk, and an optional quarterly seasonal component. Model estimation utilized INLA, with performance assessed through DIC, WAIC, mean absolute deviance, and mean squared prediction error metrics. The NB specification including quarterly seasonality significantly outperformed an equivalent model lacking seasonal terms, while coefficient estimates for fixed effects showed consistency across models. The NB size parameter indicated strong overdispersion, and the BYM2 mixing parameter suggested that roughly 90% of residual spatial variance is structured along the segment adjacency graph. Comparison of empirical and model-based zero proportions showed that the NB model with spatiotemporal random effects adequately reproduced the extreme sparsity, making a zero-inflated NB specification unnecessary. Out-of-sample validation for 2024 demonstrated low bias and good predictive performance, and risk stratification revealed that a small fraction of highway corridors accounts for a disproportionate share of observed DVCs. The proposed framework provides a practical tool for generating seasonal DVC risk maps and prioritizing corridor-level mitigation measures such as wildlife fencing, crossing structures, and targeted speed management.