Using Hierarchical Bayes draws for improving shares of choice predictions in conjoint simulations: A study based on conjoint choice data

Abstract

The use of Hierarchical Bayes (HB) estimation techniques for choice-based conjoint (CBC) data offers the opportunity to directly use HB draws for preference simulations. This paper analyzes the use of HB draws for shares of choice predictions. Five different choice rules are compared: the first choice rule applied to HB draws, the logit choice rule applied to HB draws, the randomized first choice rule, the traditional first choice rule and the traditional logit choice rule. Each two different holdout choice scenarios are constructed containing one time two extremely similar and the other time very unique alternatives to assess how well the choice rules tolerate the IIA property in predicting choice shares. We present a Monte Carlo study to systematically explore shares of choice predictions based on the different choice rules and further verify whether our findings hold in empirical settings. The key finding of our Monte Carlo study is that using HB draws either combined with the first choice rule or the logit choice rule substantially improves choice share predictions when compared to the other choice rules, regardless of the type of holdout choice scenario. While the logit choice rule applied to HB draws performs a touch better for simulated data, the first choice rule applied to HB draws provides the best choice share predictions for each of the five empirical data sets. Using HB draws does not only provide the best predictive validity but, more importantly, it is theoretically correct when applying a Bayesian estimation approach to CBC data.