Modeling school bus seat belt usage: Nested and mixed logit approaches

School bus seat belt usage has been of great interest to the school transportation community. Understanding factors that influence students' decisions about wearing seat belts or not is important in determining the most cost-effective ways to improve belt usage rate, and thus the seat belt safety benefits. This paper presents a rigorous empirical analysis on data from Alabama School Bus Pilot Project using discrete choice modeling framework. In order to collect relevant information on individual student-trips, a new data collection protocol is adopted. Three choice alternatives are considered in the study: wearing, not wearing, and improperly wearing seat belts. A student's choice probabilities of these alternatives are modeled as functions of the student's characteristics and trip attributes. The coefficients of the variables in the functions are estimated first using standard multinomial logit model. Moreover, to account for potential correlations among the three choice alternatives and individual-level preference and response heterogeneity among users, nested and mixed logit models are employed in the investigation. Eight significant influence factors are identified by the final models. Their relative impacts are also quantified. The factors include age, gender and the home county of a student, a student's trip length, time of day, seat location, presence and active involvement of bus aide, and two levels of bus driver involvement. The impact of the seat location on students' seat belt usage is revealed for the first time by this study. Both hypotheses that some of the choice alternatives are correlated and that individual-level heterogeneity exists are tested statistically significant. In view of this, the nested and the mixed logit model are recommended over the standard multinomial logit model to describe and predict students' seat belt usage behaviors. The final nested logit model uncovers a correlation between improper wearing and not wearing, indicating there are some unknown or unobserved contributing factors that are common to these two choices. In the final random-parameter mixed logit model, individual preference heterogeneity is captured by random coefficients of county variables. Individual response heterogeneity is reflected in the random effect of a driver's remarks on students' seat belt usage. Both recommended models are helpful in predicting seat belt usage rate quantitatively for given circumstances, and will provide valuable insights in practice of school transportation management.