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

Currently, there is an important debate about the relative merits of models with discrete and continuous representations of consumer heterogeneity. A recent JMR study (Andrews, Ansari, and Currim 2002, AAC hereafter) compared metric conjoint analysis models with discrete and continuous representations of heterogeneity, finding no differences between the two models with respect to parameter recovery and prediction of ratings for holdout profiles. Models with continuous representations of heterogeneity did 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 vs. continuous representations of heterogeneity in terms of the accuracy of household-level parameters, fit, and forecasting accuracy. To accomplish this goal, we 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 do fit the data better. A recent study by Andrews, Ansari, and Currim (2002) compared the relative effectiveness of models with discrete vs. continuous representations of consumer heterogeneity in the context of metric conjoint analysis. They compared finite mixture (FM) models, which describe heterogeneity with discrete distributions, and hierarchical Bayesian (HB) estimation of models with continuous representations of heterogeneity in terms of parameter recovery, fit, and prediction. The study found that FM and HB-estimated models were equally effective in recovering individual-level parameters and predicting ratings of holdout profiles, while HB-estimated models fit the data better than FM models. In addition, both model specifications were shown to be quite robust to violations of underlying assumptions. For example, an HB model with a unimodal prior performed well even when true partworths came from a mixture of distributions, and FM produced very good parameter estimates at the individual level, despite its intended usage at the segment level. The goal of the current study is to compare the relative empirical performance of logit choice models with discrete vs. continuous representations of heterogeneity under experimental conditions similar to those in the AAC study. As yet, the relative empirical advantages and disadvantages of …