An Empirical Comparison of Logit Choice Models with Discrete versus Continuous Representations of Heterogeneity

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Abstract
Currently, there is an important debate about the relative merits of models with discrete and continuous representations of consumer heterogeneity. In a recent JMR study, Andrews, Ansari, and Currim (2002 ; hereafter AAC) compared metric conjoint analysis models with discrete and continuous representations of heterogeneity and found no differences between the two models with respect to parameter recovery and prediction of ratings for holdout profiles. Models with continuous representations of heterogeneity fit the data better than models with discrete representations of heterogeneity. The goal of the current study is to compare the relative performance of logit choice models with discrete versus continuous representations of heterogeneity in terms of the accuracy of household-level parameters, fit, and forecasting accuracy. To accomplish this goal, the authors conduct an extensive simulation experiment with logit models in a scanner data context, using an experimental design based on AAC and other recent simulation studies. One of the main findings is that models with continuous and discrete representations of heterogeneity recover household-level parameter estimates and predict holdout choices about equally well except when the number of purchases per household is small, in which case the models with continuous representations perform very poorly. As in the AAC study, models with continuous representations of heterogeneity fit the data better.