Bayesian analysis of a binary choice multidimensional scaling model with correlated errors using the Gibbs sampling method.

Abstract

This dissertation presents a new Bayesian approach to likelihood-based choice multidimensional scaling vector threshold model designed to analyze "pick any/J" choice data. The relevant psychometric literature concerning the spatial treatment of such binary choice data and various sampling-based approaches are reviewed. Using a variant of the Gibbs sampler, an algorithm is developed to draw from the exact posterior of the MDS vector choice model with correlated errors. Sampling directly from the posterior distribution of the model parameters facilitates a finite-sample Bayesian analysis. This approach avoids direct evaluation of the likelihood and, thus, avoids the problems associated with correlated errors which hinder analyzing choice probabilities. An application concerning simulated and actual consumer choice data are discussed. Finally, directions for future research are presented in terms of future applications and generalizing the model using the Gibbs sampler.