A unified approach to conjoint analysis models

Abstract

We present a unified approach to conjoint analysis models using a Bayesian framework. One data source is used to form a prior distribution for the partworths, whereas full-profile evaluations under a rating scale, ranking, discrete choice, or constant-sum scale constitute the likelihood data ("one model fits all"). Standard existing models for conjoint analysis. considered in the literature. become particular cases of the proposed specification, and explicit formulas for the gains of using multiple Sources of data are presented. We demonstrate our method on a conjoint analysis dataset containing both self-explicated evaluations and constant-sum profile data on new automobiles originally collected and described by Krieger, Green, and Umesh. Our empirical findings are "mixed" in that for some out-of-sample predictive measures our Bayesian approach is superior to using profile-only or self-explicated-only data. and for other measures it is not. Our findings suggest that the primary determinant as to whether self-explicated data add information above and beyond the profile data is the degree of incongruity between the calibration and validation data formats. Specifically, when the same type of data are collected for both sources. self-explicated data add less. and vice versa. A further contribution of our Work (and one that is easily implemented, given the general nature of our approach) is that we take our data and fit constant sum, ranking, and binary choice models to it, allowing, us to infer the "change" in information when taking data and transforming its scale (a common practice). A simulation study indicates the viability of this approach. A simple Gibbs sampler simulation scheme adapted to the form of the outcome measure, using data augmentation and Metropolis sampling, is considered for inference under the model.