Investigating the Effects of Underreporting of Crash Data on Three Commonly Used Traffic Crash Severity Models: Multinomial Logit, Ordered Probit and Mixed Logit Models

Although a lot of work has been devoted to developing crash severity models to predict the probabilities of crashes for different severity levels, very few studies have considered the underreporting issue in the modeling process. Inferences about a population of interest will be biased if crash data are treated as a random sample coming from the population without considering the different unreported rates for each crash severity level. The primary objective of this study aimed at examining the effects of underreporting for three commonly used traffic crash severity models: multinomial logit (MNL), ordered probit (OP) and mixed logit (ML) models. The objective was accomplished via a Monte-Carlo approach using simulated and observed crash data. The results showed that in order to minimize the bias and reduce the variability of the model, fatal crashes should be set as the baseline severity for the MNL and ML models while, for the OP models, the rank for the crash severity should be set from fatal to propertydamage-only (PDO) in a descending order. In addition, none of the three models was immune to this underreporting issue. The results also showed that when the full or partial information about the unreported rates for each severity level is known, treating crash data as outcome-based samples in model estimation, via the Weighted Exogenous Sample Maximum Likelihood Estimator (WESMLE), dramatically improve the estimation for all three models compared to the result produced from the Maximum Likelihood estimator (MLE).