How to Generalize from a Hierarchical Model?
35 Pages Posted: 16 Aug 2017 Last revised: 26 Apr 2018
Date Written: April 17, 2018
In many marketing applications of hierarchical models the goal is to inform actions that apply to the population of consumers beyond the sample available for calibration; the goal is to generalize to the population, an exercise often referred to as market simulation. Examples are price and product optimization based on household scanner panel data or data from discrete choice experiments. It is common practice to rely on the collection of individual level posterior mean preferences of in-sample respondents, or consumers, as a representation of population preferences in this context. We show that this results in biased inferences and misleading recommendations precisely in situations that call for a hierarchical model. Generalizations that avoid this bias rely heavily on the hierarchical prior distribution, which is often only regarded as a smoothing device but not as a useful model per se. We show how to specify more economically faithful hierarchical prior distributions based on prior constraints and a marginal-conditional decomposition for the hierarchical prior distribution, and how to efficiently sample from the implied posterior. Practical relevance is demonstrated in two empirical case studies.
Keywords: Discrete Choice, Bayesian Inference, Market Simulation, Constrained Hierarchical Prior
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