The benefits of allowing heteroscedastic stochastic distributions in multiple discrete-continuous choice models

Abstract

This paper investigates the benefits of incorporating heteroscedastic stochastic distributions in random utility maximization-based multiple discrete-continuous (MDC) choice models. To this end, first, a Multiple Discrete-Continuous Heteroscedastic Extreme Value (MDCHEV) model is formulated to allow heteroscedastic extreme value stochastic distributions in MDC models. Next, an empirical analysis of individuals' daily time use choices is carried out using data from the National Household Travel Survey (NHTS) for three geographical regions in Florida. A variety of different MDC model structures are estimated: (a) the Multiple Discrete-Continuous Extreme Value (MDCEV) model with independent and identically distributed (IID) extreme value error structure, (b) the MDCHEV model, (c) the mixed-MDCEV model that allows heteroscedasticity by mixing a heteroscedastic distribution over an IID extreme value kernel, (d) the MDC generalized extreme value (MDCGEV) model that allows inter-alternative correlations using the multivariate extreme value error structure, (e) the mixed-MDCEV model that allows inter-alternative correlations using common mixing distributions across choice alternatives, and (f) the mixed-MDCEV model that allows both heteroscedasticity and inter-alternative correlations. Among all these model structures, the MDCHEV model provided the best fit to the current empirical data. Further, heteroscedasticity was prominent while no significant inter-alternative correlations were found. Specifically, the MDCHEV parameter estimates revealed the significant presence of heteroscedasticity in the random utility components of different activity type choice alternatives. On the other hand, the MDCEV model resulted in inferior model fit and systematic discrepancies between the observed and predicted distributions of time allocations, which can be traced to the thick right tail of the type-1 extreme value distribution. The MDCHEV model addressed these issues to a considerable extent by allowing tighter stochastic distributions for certain choice alternatives, thanks to its accommodation of heteroscedasticity among random utility components. Furthermore, spatial transferability assessments using different transferability metrics also suggest that the MDCHEV model clearly outperformed the MDCEV model.