Modelling low temporal, large spatial data of fatal crashes: An application of negative binomial GSARIMAX time series

Road traffic injuries represent a critical public health concern, particularly in developing nations such as Iran, where the incidence of fatal crashes is escalating. Addressing this issue effectively requires sophisticated analytical methodologies to elucidate and mitigate the multifaceted factors contributing to traffic fatalities. This study introduces the Negative Binomial Generalized Seasonal Autoregressive Integrated Moving Average with Exogenous Variables (GSARIMAX) model as an innovative approach for analyzing low temporal (daily) and large spatial count data of fatal crashes over a ten-year period (March 2014 to March 2022) in Iran. Unlike traditional models that predominantly focus on aggregated monthly or high-resolution data, the proposed negative binomial GSARIMAX model leverages daily count data, accommodating over-dispersion inherent in crash counts and providing a more granular and accurate analysis across extensive spatial regions. The model integrates significant exogenous variables, including traffic volume, maximum and minimum temperatures, wind speed, and wind direction, alongside harmonic seasonal components to capture both annual and semi-annual periodic fluctuations in crash occurrences. Model performance was rigorously evaluated using Deviance Information Criterion (DIC) and Mean Absolute Relative Error (MARE) metrics, alongside out-of-sample predictive accuracy assessments. The negative binomial GSARIMAX (0,1,2)-SOH model demonstrated superior performance compared to the Gaussian GSARIMAX counterpart, evidenced by lower MARE and DIC values. Notably, traffic volume and maximum temperature emerged as significant predictors of fatal crashes, while seasonal harmonic terms further enhanced model accuracy by effectively capturing temporal dynamics. The Bayesian estimation framework employed facilitates robust inference and the analysis of posterior predictive distributions, affirming the Negative Binomial GSARIMAX model's superior fit and forecasting capabilities. These findings underscore the model's potential advantages over conventional Gaussian statistical methods, particularly in handling low temporal resolution and large spatial datasets. Moreover, dynamic models incorporating exogenous variables demonstrated enhanced predictive performance, highlighting the importance of integrating diverse factors in crash analysis. This study not only advances the methodological landscape for traffic crash analysis but also provides actionable insights for policymakers and safety authorities. By identifying key determinants of fatal crashes and accounting for seasonal variations, the Negative Binomial GSARIMAX model serves as a valuable tool for informing targeted interventions aimed at reducing traffic fatalities. Future research should extend this approach by incorporating additional environmental and behavioral variables and conducting comparative analyses across multiple provinces to capture a broader spectrum of influencing conditions.