Accommodating Taste and Scale Heterogeneity for Front-Seat Passenger’ Choice of Seat Belt Usage

Mahdi Rezapour,Khaled Ksaibati

doi:10.3390/math9050460

Abstract

There is growing interest in implementation of the mixed model to account for heterogeneity across population observations. However, it has been argued that the assumption of independent and identically distributed (i.i.d) error terms might not be realistic, and for some observations the scale of the error is greater than others. Consequently, that might result in the error terms’ scale to be varied across those observations. As the standard mixed model could not account for the aforementioned attribute of the observations, extended model, allowing for scale heterogeneity, has been proposed to relax the equal error terms across observations. Thus, in this study we extended the mixed model to the model with heterogeneity in scale, or generalized multinomial logit model (GMNL), to see if accounting for the scale heterogeneity, by adding more flexibility to the distribution, would result in an improvement in the model fit. The study used the choice data related to wearing seat belt across front-seat passengers in Wyoming, with all attributes being individual-specific. The results highlighted that although the effect of the scale parameter was significant, the scale effect was trivial, and accounting for the effect at the cost of added parameters would result in a loss of model fit compared with the standard mixed model. Besides considering the standard mixed and the GMNL, the models with correlated random parameters were considered. The results highlighted that despite having significant correlation across the majority of the random parameters, the goodness of fits favors more parsimonious models with no correlation. The results of this study are specific to the dataset used in this study, and due to the possible fact that the heterogeneity in observations related to the front-seat passengers seat belt use might not be extreme, and do not require extra layer to account for the scale heterogeneity, or accounting for the scale heterogeneity at the cost of added parameters might not be required. Extensive discussion has been made in the content of this paper about the model parameters’ estimations and the mathematical formulation of the methods.

Highlights

Introduction published maps and institutional affilMore than 37,000 people died in highway crashes in the U.S in 2017 alone, of which47% were not wearing seat belt [1]
Correlated random parameters of the generalized multinomial logit model (GMNL) and the mixed logit (MIXL) were considered for comparison purposes
It has been discussed that the performance of GMNL and MIXL or scale multinomial logit (SMNL) are dependent on the complexity of the data [12], suggesting more sophisticated models would not necessarily result in a better fit

Summary

Introduction

47% were not wearing seat belt [1]. Seat belt usage could reduce both fatal and non-fatal injuries by 60% among front-seat occupants, and 44% for rear seat occupants [2]. Despite efforts regarding the importance of seat belt usage, a significant portion of vehicle users do not buckle up. The number of passengers that do not wear seat belts is much higher compared to the drivers. In Wyoming, more than 80% of drivers buckle up but less than 50% of the passengers used seat belt while getting ride. It is known that the individuals would base their choices about wearing seat belt based on various attributes, which might show itself with substantial heterogeneity. The main drawback of not accounting for that heterogeneity is linked to biased, and often erroneous estimates of the attributes, and lack of understanding of underlying effects of the point estimates

Objectives

Methods

Results

Conclusion