A Low-Dimension Shrinkage Approach to Choice-Based Conjoint Estimation

Estimating consumers' heterogeneous preferences using choice-based conjoint (CBC) data poses a considerable modeling challenge, as the amount of information elicited from each consumer is often limited. Given the lack of individual-level information, effective information pooling across consumers becomes critical for accurate CBC estimation. In this paper, we propose an innovative low-dimension shrinkage approach to pooling information and modeling preference heterogeneity, in which we learn a low-dimensional affine subspace approximation of the heterogeneity distribution and shrink the individual-level part-worth estimates toward this affine subspace. Drawing on recent modeling techniques for low-rank matrix recovery, we develop a computationally tractable machine learning model for implementing this low-dimension shrinkage and apply it to CBC estimation. We use an extensive simulation experiment and a field data set to demonstrate the superior performance of our low-dimension shrinkage approach as compared to alternative benchmark models.