Spatial autocorrelation and skewed distribution are the most frequent issues in crash rate modelling analysis. Previous studies commonly focus on the spatial autocorrelation between adjacent regions or the relationships between crash rate and potentially risky factors across different quantiles of crash rate distribution, but rarely both. To overcome the research gap, this study utilizes the spatial autoregressive quantile (SARQ) model to estimate how contributing factors influence the total and fatal-plus-injury crash rates and how modelling relationships change across the distribution of crash rates considering the effects of spatial autocorrelation. Three types of explanatory variables, i.e., demographic, traffic networks and volumes, and land-use patterns, were considered. Using data collected in New York City from 2017 to 2019, the results show that: (1) the SARQ model outperforms the traditional quantile regression model in prediction and fitting performance; (2) the effects of variables vary with the quantiles, mainly classifying three types: increasing, unchanged, and U-shaped; (3) at the high tail of crash rate distribution, the effects commonly have sudden increases/decrease. The findings are expected to provide strategies for reducing the crash rate and improving road traffic safety.

Secondary crashes (SCs) are typically defined as the crash that occurs within the spatiotemporal boundaries of the impact area of the primary crashes (PCs), which will intensify traffic congestion and induce a series of road safety issues. Predicting and analyzing the time and distance gaps between the SCs and PCs will help to prevent the occurrence of SCs. In this paper, a combined data-driven method of static and dynamic approaches is applied to identify SCs. Then, the random forests (RF) method is implemented to predict the two gaps using temporal, primary crash, roadway, and real-time traffic characteristics data collected from 2016 to 2019 at California interstate freeways. Subsequently, the SHapley Additive explanation (SHAP) approach is employed to interpret the RF outputs. The results show that the traffic volume, speed, lighting, and population are considered the most significant factors in both gaps. Furthermore, the main and interaction effects of factors are also quantified. High volume possibly promotes the time and distance gaps, while low volume inhibits them. And volume affects the distance gap inconsiderably when it falls between 300 and 400 veh/5 min. Traffic conditions with high speed and low volume are strongly associated with short-time and short-distance gaps. Darker surroundings probably accelerate the occurrence of SCs. Moreover, crashes involving the violation categories of improper turns or unsafe lane changes likely result in long time and distance gaps. These results have important implications for proposing traffic management and improving road safety.