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Two-lane highways represent the majority of highways in the U.S. and their safety is of crucial concern. Even though road safety researchers intensively evaluated two-lane highway safety, past studies were challenged by a methodological hindrance, namely that of correlated random parameters (CRP) modeling methods. Random parameters models capture unobserved heterogeneity effects of crash contributing factors, while CRP models offer the additional benefit of capturing correlations among variables inducing such unobserved heterogeneity effects. However, CRP models do not permit specifying pairs of regressors, with statistically insignificant correlations, to be uncorrelated. In this research, it was demonstrated that the conventional uncorrelated random parameters ordinal probit (URPOP) structure with interaction effects outperformed the correlated random parameters ordinal probit (CRPOP) structure when modeling injury severity risks of two-lane highway crashes in Wyoming. As per the former model’s results, speeding, head-on collisions, sideswipe opposite-direction collisions, intersecting-direction collisions, motorcycle involvement, impaired driving, distracted driving, the interaction effect of speeding with motorcycle involvement, that of head-on collisions with impaired driving, and that of head-on collisions with commercial vehicle involvement all raised the likelihood of sustaining severe injuries. Conversely, leaving the crash scene, proper seat belt use, wet road surfaces, and the interaction effect of impaired driving with motorcycle involvement alleviated the risk of incurring severe injuries. The superiority of the proposed model and its reduced computation time warrant its recommendation for implementation in future studies. Also, from a practical perspective, safety mitigation measures are suggested based on this research’s findings.

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