Bayesian confirmatory analysis of multiple response data

This paper proposes a Bayesian confirmatory factor-analytic probit model to reveal the latent utility structure of multiple response data commonly found in marketing surveys. It conditions model formulation on previous knowledge and imposes a parsimonious hierarchical structure involving a measurement model (to define common factors) and a structural model to explain brand choice. The confirmatory model offers some advantages over exploratory models applied to multiple response survey data. First, the model improves model identification and prediction by imposing a simpler structure that accounts for data dependencies without assuming a multivariate distribution. Secondly, using MCMC estimation, the model can easily accommodate many underlying dimensions (J) in the data, which has been challenging to address with other approaches. Lastly, the confirmatory approach offers a practical framework where the analyst has control over the specification of the latent structure of the data via informative priors. This study uniquely applies the model to test and ‘confirm’ previous knowledge and managerial hypotheses about market structures, and how brands are related and compete with one another. The study applies a fully Bayesian estimation and model choice strategy and includes a cross-validatory demarcation between test and validation sub-samples.