Choice models with stochastic variables and random coefficients

In travel choice models, variables describing alternative attributes such as travel time may have to be specified as stochastic because the analyst may not have accurate measurements of the attribute values considered by the decision-maker. Such stochasticity in alternative attributes is different from unobserved heterogeneity in the coefficients representing travellers' response to those attributes. Specifying only one of these as random while keeping the other fixed can potentially result in biased parameter estimates, inferior goodness-of-fit, and distorted information for policy analysis. Therefore, in this study, we propose an integrated choice and stochastic variable modelling framework with random coefficients (i.e., an ICSV-RC framework) that allows the analyst to accommodate stochasticity in alternative attributes and random coefficients on such attributes. In addition, we show that ignoring either source of stochasticity - stochasticity in alternative attributes or unobserved heterogeneity in response to the attributes - results in models with inferior goodness-of-fit and a systematic bias in all parameter estimates. We demonstrate this using simulation experiments for two different travel choice settings, one involving labelled mode choice alternatives and the other involving unlabelled route choice alternatives. In addition, we present an empirical analysis in the context of truck route choice to highlight the importance of accommodating both sources of variability - stochasticity in travel times and random heterogeneity in response to travel times.