Does scale heterogeneity across individuals matter? An empirical assessment of alternative logit models

There is growing interest in establishing a mechanism to account for scale heterogeneity across individuals (essentially the variance of a variance term or the standard deviation of utility over different choice situations), in addition to the more commonly identified taste heterogeneity in mixed logit models. A number of authors have recently proposed a model that recognizes the relationship between scale and taste heterogeneity, and investigated the behavioural implications of accounting for scale heterogeneity in contrast to a term in the utility function, itself. In this paper we present a general model that extends the mixed logit model to explicitly account for scale heterogeneity in the presence of preference heterogeneity, and compare it with models that assume only scale heterogeneity (referred to as the scale heterogeneous multinomial logit model) and only preference heterogeneity. Our empirical assessment suggests that accommodating scale heterogeneity in the absence of accounting for preference heterogeneity may be of limited empirical interest, resulting in a statistically inferior model, despite it being an improvement over the standard MNL model. Scale heterogeneity in the presence of preference heterogeneity does garner favour, with the generalized mixed logit model an improvement over the standard mixed logit model. The evidence herein suggests, however, that compared to a failure to account for preference heterogeneity that is consequential, failure to account for scale heterogeneity may not be of such great empirical consequence in respect of behavioural outputs such as direct elasticities and willingness to pay. However additional studies are required to establish the extent to which this evidence is transferable to a body of studies.