Spatial heterogeneity constitutes an essential element in advanced crash frequency modeling frameworks. However, current spatial methodologies exhibit two primary limitations: (1) inflexible parametric formulations of exposure variables, and (2) non-conjugate model structures that compromise Gibbs sampler convergence. To address these issues, we develop a semi-parametric spatial count model that introduces flexible exposure specifications, requiring only monotonic functional relationships while explicitly incorporating spatial dependence. This framework employs data-augmented Gibbs sampling to achieve computationally efficient Bayesian estimation through conjugate forms. Simulation results verified that the estimation works as intended. Empirical evaluations across Houston and Dallas urban road networks demonstrated significant performance advantages relative to conventional approaches. Integration of estimates with roadway characteristics and exposure metrics yielded substantive insights into crash patterns within adjacent roadway segments. Road crash analysis in both cities showed three key patterns. First, segment length consistently serves as an offset variable, while annual average daily traffic (AADT) displays complex, segment-varying relationships due to unobserved heterogeneity. In Houston, the effect of AADT on crashes weakens under low traffic volumes but becomes nearly proportional (offset-like) at medium-to-high volumes. Conversely, Dallas exhibits more linear patterns, suggesting city-specific heterogeneity. Second, compared to one-way highway design, other designs generally pose higher risks, with lane number, width, and roadbed width increasing risk to different degrees, while better median designs reduce risk. Finally, both cities exhibit strong spatial heterogeneity in crash count. This framework enables transportation agencies to prioritize road safety interventions through precise quantification of crash risk factors and spatial heterogeneity, while avoiding restrictive parametric assumptions.
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