Modeling price response from retail sales: An empirical comparison of models with different representations of heterogeneity

We assess the performance of store sales models with discrete versus continuous representations of heterogeneity. Specifically, we compare the general heterogeneity model introduced by Allenby et al. (1998) and Lenk and DeSarbo (2000) to its nested versions, a homogeneous model ignoring heterogeneity in marketing effects, a hierarchical Bayes model and a latent class model within a fully Bayesian framework. In an empirical application with scanner data of a large retail chain, we analyze the possible improvements in model fit and predictive validity for approaches that allow for heterogeneity compared to the homogeneous model, and illustrate differences between the various model versions regarding price elasticities. We further compare the performance of the different models to the zone pricing model practiced by the retailer. We find that the more parsimonious models with discrete representations of heterogeneity clearly outperform their continuous counterparts in terms of the model likelihood. Moreover, incorporating heterogeneity does not improve the model fit for many brands compared to the homogeneous model. The prediction accuracy of models with discrete representations of heterogeneity is comparable or even superior to that of continuous heterogeneity models. Noticeably, the predictive performance of the retailer’s zone model is considerably worse than that of the best model for the majority of brands. Our empirical study further demonstrates that models with different representations of heterogeneity provide similar implications for price elasticities, suggesting that there is little benefit from using more complex continuous heterogeneity models from a managerial point of view, at least for the present data.