Accounting for unobserved heterogeneity and spatial instability in the analysis of crash injury-severity at highway-rail grade crossings: A random parameters with heterogeneity in the means and variances approach

Crashes at highway-rail grade crossings often result in higher proportion of injury and fatality of the vehicle occupants as compared to other crash types, necessitating in-depth investigation to identify their causal factors. In this study, injury-severity outcomes from highway-rail grade crossing crashes are analyzed using crash data from Texas and California, which are the most vulnerable states in the United States, in terms of highway-rail grade crossing crash occurrences. The data are collected from the Federal Railroad Administration’s (FRA) Office of Safety Analysis, covering a period between 2012 and 2020. Such data often suffer from out-of-date or missing information due to cost and available resources limitations, which inevitably may lead to unobserved characteristics varying systematically across various aspects of the data. Unobserved heterogeneity is an important misspecification issue, that in turn introduces modeling bias. To address these limitations, the random parameters multinomial logit modeling framework with heterogeneity in the means and variances is employed for the econometric analysis in this paper, which effectively accounts for multilayered unobserved heterogeneity. Spatial instability of the factors affecting different injury-severity levels is investigated as well. The results indicate that the factors are not spatially stable across Texas and California, leading to the estimation of two separate state-specific models. The estimation results of the two state-specific models help identify several vehicle-, train-, vehicle driver-, weather- and crossing-specific factors affecting different injury severity outcomes. Moreover, the results also demonstrate the varying magnitude of the identified factors on injury-severity across the two states, indicating the presence of spatial instability. The findings of this study highlight the importance of accounting for unobserved heterogeneity and spatial instability to avert critical methodological issues and misleading inferences from the simple aggregation used in most econometric analysis of highway-rail grade crossing crashes.