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 severe crashes (KA) and the frequency of non-severe crashes (BCO). To address this research gap, the current study introduces a copula-based joint modeling framework designed to analyze these two dimensions of arterial segment safety. Specifically, the proposed model integrates a binary logit model for estimating arterial segments potential for severe (KA) crashes and a negative binomial model for the frequency of non-severe (BCO) crashes. 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 collected from District 5, Florida for the years 2016 to 2024. 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 analysis are also conducted to quantify the impact of explanatory variables on both risk classification and non-severe 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 frequency of KA crashes is strongly associated with the occurrence of BCO events. The contributing factors remain largely consistent across both models, when KA and BCO are modeled separately. The findings from this research can provide transportation agencies with valuable insights into improving arterial segment safety through targeted interventions.