Joint Modeling of Segment-Level Crash Risk and Frequency on Arterials: A Copula-Based Framework with Temporal Instability

Enhancing the safety of arterial roads is critical due to their role in accommodating high traffic volumes and serving as key connectors within transportation networks. Traditional safety analyses often overlook the potential relationship between factors influencing segment-level risk classification for fatal and incapacitating injury crashes (KA) and the frequency of nonsevere crashes involving non-incapacitating injuries, possible injuries, and no injury (BCO). To address this gap, this study proposes a copula-based joint modeling framework integrating a binary logit model for estimating arterial segments potential for KA crashes and a negative binomial model for BCO crash frequency. The dependency between these two outcomes is captured using a closed-form flexible copula framework. Testing various copula; the Frank copula showed improved fit. The data for this analysis is from District 5, Florida (2016–24). Temporal instability of the variables is explicitly addressed using a pooled spline formulation approach dividing by the dataset into three distinct periods, each consisting of three years of crash data. Elasticity analyses are also conducted to quantify the impact of explanatory variables on both risk classification and nonsevere crash frequency. Key findings indicate that higher traffic volumes, three or more lanes per direction, and urban roadway type significantly increase both KA risk classification and BCO crash frequency, while adequate shoulder width and paved shoulder type reduce these risks. Moreover, the contributing factors remain largely consistent across both models, when KA and BCO are modeled separately. The findings provide transportation agencies with actionable insights for improving arterial segment safety through enhanced network screening, refined prioritization, and targeted safety interventions.