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

Conventional random-coefficients models of conditional brand choice using panel data ignore the de-pendence 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 alter-native 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 sim-ulated 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