Investigating unobserved heterogeneity in factors of fatal and injury crashes across Italian secondary road networks: Fixed and random parameters approach

Developing Safety Performance Functions (SPFs) and Crash Modification Factors (CMFs) represent one of the leading approaches for determining how infrastructure-related features impact crash likelihood. In Italy, few works investigated the causes of crash occurrences on secondary road networks, i.e., minor rural, suburban, and urban two-lane roads, connecting the primary road network (freeways and highways) with local roads. Furthermore, to the best of our knowledge, no studies addressed the issue of spatial unobserved heterogeneity in factors contributing to crash occurrence on secondary roads in Italy. To fill this gap and intending to provide an in-depth analysis of causes of Fatal and Injury (FI) crashes that occur on such networks, this paper proposes the development of SPFs and related CMFs across 905 km of Italian secondary roads. Incorporating geometrical, functional, and road context information, a Negative Binomial Regression with Fixed Parameters (FP-NBR) and Random Parameters (RP-NBR) to account for unobserved heterogeneity have been adopted for fitting 5,792 FI crashes that occurred within 2008–2016. Capturing unobserved heterogeneity affecting some of the factors, outcomes show that the RP-NBR markedly outperforms the FP-NBR in terms of predictive performance. Conversely, the latter shows a higher level of interpretation. Elasticities and CMFs indicate that traffic flow, carriageway width, driveway density, the density of intersections, and road area type are the most influential parameters, whereas longitudinal gradient and road alignment have a weaker effect on FI occurrences. These SPFs and related CMFs can improve planning activity, as well as monitoring and maintenance interventions across secondary road networks.