Incorporating spatial relationship between curves to account for unobserved heterogeneity in severe crashes on mountainous curves using latent class clustering and Firth’s logistic regression

Analyzing curve-based crashes by neglecting underlying spatial relationships can lead to significant unobserved heterogeneity. A two-step latent class clustering framework was adopted to account for unobserved heterogeneity in crash severity on mountainous curves, incorporating curve design parameters and spatial relationships. An optimal number of clusters were determined followed by a swap-stepwise algorithm for selecting the most important contributors to the clustering process. Cluster-specific models were then developed using Firth’s logistic regression due to restricted sample size. Marginal effects revealed that while run-off-the-road and two wheelers invariably increased severity, cluster-specific effects showed that narrow and intermediately wide pavements increased crash severity by 13.77% and 11.45%, respectively, while dark conditions and age≥50 years reduced it by 14.53% and 12.44%, respectively. A very sharp approach curve with short length increased severity by 12.25%, reinforcing the role of spatial relationship. The findings can assist in designing and implementing more actionable safety interventions.