A Hierarchical Bayes Model for Ranked Conjoint Data

This paper investigates the adequacy of the hierarchical Bayes (HB) model for rankbased conjoint data. While recent research has demonstrated the robustness of the HB model compared to traditional estimation methods for rank based conjoint models, we conduct an indepth analysis of the underlying reasons of these findings. Hereby we investigate the fundamental assumptions of rank based conjoint models in order to explain problems concerning information loss by using ranking methods. In particular, we expose the ambiguity of rank orders and the inherent ambiguity of part-worth estimates. Propositions conform to requisite traits postulated by the model of rank based conjoint data are elaborated. We point out existing shortfalls of traditional estimation methods since they do not fulfill the requirements of rank based conjoint data. In contrast, the HB model explicitly involves the stochastic modeling of deviations at individual and super-population level. Thus we postulate a superior adequacy of the HB model versus OLS and LINMAP. In order to investigate this hypothesis, a comparison of the estimation accuracy is performed by using simulated data. The simulation results show the superiority of the HB model in terms of minimizing the absolute deviations of part-worth estimates from their true values and consequently in generating parameters which reflect the true nature of the data.