Addressing unobserved heterogeneity in the analysis of bicycle crash injuries in Scotland: A correlated random parameters ordered probit approach with heterogeneity in means

This paper investigates the determinants of injury severities in single-bicycle and bicycle-motor vehicle crashes by estimating correlated random parameter ordered probit models with heterogeneity in the means. This modeling approach extends the frontier of the conventional random parameters by capturing the likely correlations among the random parameters and relaxing the fixed nature of the means for the mixing distributions of the random parameters. The empirical analysis was based on a publicly available database of police crash reports in the UK using information from crashes occurred on urban and rural carriageways of Scotland between 2010 and 2018. The model estimation results show that various crash, road, location, weather, and driver or cyclist characteristics affect the injury severities for both categories of crashes. The heterogeneity-in-the-means structure allowed the incorporation of a distinct layer of heterogeneity in the statistical analysis, as the means of the random parameters were found to vary as a function of crash or driver/cyclist characteristics. The correlation of the random parameters enabled the identification of complex interactive effects of the unobserved characteristics captured by road, location and environmental factors. Overall, the determinants of injury severities are found to vary between single-bicycle and bicycle-motor vehicle crashes, whereas a number of common determinants are associated with different effects in terms of magnitude and sign. The comparison of the proposed methodological framework with less sophisticated ordered probit models demonstrated its relative benefits in terms of statistical fit, explanatory power and forecasting accuracy as well as its potential to capture unobserved heterogeneity to a greater extent.