Hierarchical Bayes Choice Model

Hierarchical Bayes (HB) choice models estimate a separate set of preference weights — partworths — for every individual respondent, while borrowing strength across respondents through a shared population distribution. The model has two levels: at the lower level each person's choices follow a logit driven by their own coefficients, and at the upper level those individual coefficients are treated as draws from a common multivariate distribution whose mean and covariance are themselves estimated. Inference is Bayesian and proceeds by Markov chain Monte Carlo — typically Gibbs sampling with Metropolis steps — which yields a full posterior for each respondent's partworths rather than a single point estimate. The approach, codified by Rossi, Allenby, and McCulloch, solved a long-standing problem in choice modeling: how to recover genuine individual-level heterogeneity from the sparse data each person provides. Sparse individual estimates are stabilized by shrinkage toward the population mean, giving reliable person-level coefficients usable for segmentation, targeting, and realistic market simulation. HB is now the default estimator for conjoint and scanner-based choice analysis.