Purchase-Frequency Bias in Random-Coefficients Brand-Choice Models

Conventional random-coefficients models of conditional brand choice using panel data ignore the dependence of the random-coefficients distribution on the purchase frequencies. We show that this leads to biased estimates and propose a conditional likelihood approach to obtain unbiased estimates. Unlike alternative approaches that require observation of “no-purchase” occasions, our proposed method relies only on purchase data. Furthermore, our approach does not require that the researcher specify the distribution of purchase frequencies. As a result, estimates of the brand-choice model are unaffected by misspecification of the model of purchase frequencies. We demonstrate the performance of the proposed approach in simulated data and in scanner data. We find that results differ substantively from the conventional latent-class model in terms of segment membership probabilities, segment characteristics, and price elasticities.