Bayesian Statistics and Marketing, 2nd Edition

5Hierarchical Models for Heterogeneous Units

Abstract

This chapter provides a comprehensive treatment of hierarchical models. Hierarchical models are designed to measure differences between units using a particular prior structure. Choice of the form of the hierarchical model (i.e. the form of the prior) as well as the MCMC algorithm to conduct inference are important questions. We explore a new class of hybrid MCMC algorithms that are customized or tuned to the posteriors for individual units. We also implement a mixture of normals prior for the distribution of model coefficients across units. We illustrate these methods in the context of a panel of household purchase data and a base or unit‐level multinomial logit model. Those interested in the main points without technical details are urged to concentrate on Sections 5.1, 5.2, 5.4, and 5.5.3.

One of the greatest challenges in marketing is to understand the diversity of preferences and sensitivities that exists in the market. Heterogeneity in preferences gives rise to differentiated product offerings, market segments, and market niches. Differing sensitivities are the basis for targeted communication programs and promotions. As consumer preferences and sensitivities become more diverse, it becomes less and less efficient to consider the market in the aggregate. Marketing practices that are designed to respond to consumer differences require an inference method and model capable of producing individual or unit level parameter ...