Analysis and Prediction of Accident Frequency During Peak Hours at Urban Intersections Using the Random-Effects Negative Binomial (RENB) Model

This study aimed to predict crash frequency during daily peak hours at urban intersections using a Random-Effects Negative Binomial (RENB) model. The dataset comprised crash records from 34 urban intersections in Borujerd, Iran, covering a five-year period from 2021 to 2025 (corresponding to the Iranian calendar years 1400–1404). After aggregating the data on an hourly basis, the final dataset consisted of 204 observations and 698 reported crashes. The explanatory variables included hourly traffic volumes on major and minor roads, the number of intersection approaches, the number of traffic signals, and dummy variables representing peak-hour periods. Statistical analysis confirmed the presence of significant overdispersion in the crash data. Moreover, the relatively low proportion of zero-count observations indicated that the Negative Binomial model was more appropriate than zero-inflated alternatives. A comparison between the conventional Negative Binomial (NB) model and the Random-Effects Negative Binomial (RENB) model, based on the Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), and Likelihood Ratio (LR) test, demonstrated that incorporating random effects significantly improved model performance. The results revealed that traffic volume on minor roads had a greater impact on crash frequency than traffic volume on major roads. Specifically, an increase of 1,000 vehicles per hour on the minor road was associated with an approximately 146% increase in the expected crash frequency. Furthermore, increasing the number of intersection approaches from three to four resulted in a 76% increase in the expected crash frequency.