The analysis of vehicle crash injury-severity data: A Markov switching approach with road-segment heterogeneity

• A Markov-switching random parameters ordered probit model is developed for modeling highway crash injury severity data.
• A data augmented Markov Chain Monte Carlo algorithm is developed to facilitate non-linear model estimation.
• Two roadway safety states are found to exist, with the transition between these two states following a Markov process.
• Results show the proposed model has great potential for addressing unobserved heterogeneity in variety of problems.

Time-constant assumptions in discrete-response heterogeneity models can often be violated. To address this, a time-varying heterogeneity approach to model unobserved heterogeneity in ordered response data is considered. A Markov switching random parameters structure (which accounts for heterogeneity across observations) is proposed to accommodate both time-varying and time-constant (cross-sectional) unobserved heterogeneity in an ordered discrete-response probability model. A data augmented Markov Chain Monte Carlo algorithm for non-linear model estimation is developed to facilitate model estimation. The performance of the cross-sectional heterogeneity model and time-varying heterogeneity model are examined with vehicle crash-injury severity data. The time-varying heterogeneity model (Markov switching random parameters ordered probit) is found to provide the best overall model fit. Two roadway safety states are shown to exist and roadway segments transition between these two states according to Markov transition probabilities. The results demonstrate considerable promise for Markov switching models in a wide variety of applications.