Bayesian estimation of random utility models

This chapter reviews the Bayesian analysis of random utility models (RUM) for conjoint analysis. The economic theory of conjoint analysis and Bayesian estimation are remarkably related because the foundation of Bayesian decision theory derives subjective probabilities and utilities from preferences for random gambles. Bayesian estimation and prediction updates these probabilities when new information becomes available. The chapter presets the Bayesian analysis and Markov chain Monte Carlo (MCMC) estimation algorithms for a series of conjoint elicitation methods that result in continuous, ordinal, or nominal measurements. Metric conjoint requires subjects to rate product or service profiles (descriptions), thus eliciting continuous measures of the subjects’ utilities. Hierarchical Bayes models allow the profiles’ attribute partworths (coefficients) to be subject-specific and to vary with context or subjects’ covariates. Non-metric conjoint presents subjects with multiple sets consisting of two or more profiles. Subjects rank the profiles in each set in ordinal conjoint or pick the best profile in each set in nominal conjoint. The MCMC algorithm for non-metric conjoint merely adds a procedure to metric conjoint that converts the ordinal or nominal data to continuous latent utility estimates. The chapter ends with Bayesian hypothesis testing and model selection.