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

Consumers ’ heterogeneous preferences can often be represented using a multimodal continuous heterogeneity (MCH) distribution. One interpretation of MCH is that the consumer population consists of a few distinct segments, each of which contains a heterogeneous sub-population. Modeling of MCH raises considerable challenges as both across- and within-segment heterogeneity need to be accounted for. We propose an innovative sparse learning approach for modeling MCH and apply it to conjoint analysis where adequate modeling of consumer heterogeneity is critical. The sparse learning approach models MCH via a two-stage divide-and-conquer framework, in which we first decompose the consumer population by recovering a set of candidate segmentations using structured sparsity modeling, and then use each candidate segmentation to develop a set of individual-level representations of MCH. We select the optimal individual-level representation of MCH and the corresponding optimal candidate segmentation using cross-validation. Two notable features of our approach are that it accommodates both across- and within-segment heterogeneity and endogenously imposes an adequate amount of shrinkage to recover the individual-level partworths. We empirically validate the performance of the sparse learning approach using extensive simulation experiments and two empirical conjoint data sets