Modeling Multimodal Continuous Heterogeneity in Conjoint Analysis—A Sparse Learning Approach

Consumers’ preferences can often be represented using a multimodal continuous heterogeneity distribution. One explanation for such a preference distribution is that consumers belong to a few distinct segments, with preferences of consumers in each segment being heterogeneous and unimodal. We propose an innovative approach for modeling such multimodal distributions that builds on recent advances in sparse learning and optimization. We apply the model to conjoint analysis where consumer heterogeneity plays a critical role in determining optimal marketing decisions. Our approach uses a two-stage divide-and-conquer framework, where we first divide the consumer population into segments by recovering a set of candidate segmentations using sparsity modeling, and then use each candidate segmentation to develop a set of individual-level heterogeneity representations. We select the optimal individual-level heterogeneity representation using cross-validation. Using extensive simulation experiments and three field data sets, we show the superior performance of our sparse learning model compared to benchmark models including the finite mixture model and the Bayesian normal component mixture model.