Comparing Three Commonly Used Crash Severity Models on Sample Size Requirements: Multinomial Logit, Ordered Probit and Mixed Logit Models

There have been many studies that have documented the application of crash severity models to explore the relationship between accident severity and its contributing factors. Although a large amount of work has been done on different types of models, no research has been conducted about quantifying the sample size requirements for crash severity modeling. Similar to count data models, small data sets could significantly influence model performance. The objective of this study is therefore to examine the effects of sample size for the three most commonly used crash severity models: multinomial logit, ordered probit and mixed logit models. The study objective is accomplished via a Monte-Carlo approach using simulated and observed crash data. The results of this study are consistent with prior expectations in that small sample sizes significantly affect the development of crash severity models, no matter which type is used. Furthermore, among the three models, the mixed logit model requires the largest sample size, while the ordered probit model requires the lowest sample size. The sample size requirement for the multinomial logit model is located between these two models.