A Bayesian Dynamic Model for Incomplete Preferences with No-Choice Options in Conjoint Analysis

Abstract

In the analysis of ranking data such as ranking based conjoint analysis, it is common that all preference ranks are obtained in each trial. However, if there is an no-choice option in alternatives such as conjoint profiles, the ranking ends there, and partial ranking data with a structure depending on the individuals and the trials is observed. We propose a rank-ordered logit model and Bayesian estimation method for partial ranking data with no-choice options that have different ranking structures for each individual and trial. In the model, we consider the latent variables that vary according to each individual and time and decompose them into individual and temporal heterogeneity. Specifically, we consider individuals' heterogeneities using a hierarchical Bayesian model, individuals' learning and evolution of preference using a dynamic linear model, and estimate parameters via the Markov chain Monte Carlo method. For empirical analysis, we apply the proposed model to the analysis of the ranking data obtained by the conjoint measurement method. From the results of conjoint data analysis for smartphones, it is confirmed that the preference or relative importance of the attributes change among trials.