A Convex Optimization Approach to Modeling Consumer Heterogeneity in Conjoint Estimation (Revision 1 )

The authors propose and test a new approach for modeling consumer heterogeneity in conjoint estimation, which extends individual-level methods based on convex optimization and statistical machine learning. The authors develop methods both for metric and choice data. Like HB, their methods shrink individual-level partworth estimates towards a population mean. However, while HB samples from a posterior distribution that depends on exogenous parameters (the parameters of the second-stage priors), the authors minimize a convex loss function that depends on an endogenous parameter (determined from the calibration data using cross-validation). As a result, the amounts of shrinkage differ between the two approaches, leading to different estimation accuracies. Comparisons based on simulations as well as empirical data sets suggest that the new approach overall outperforms standard HB (i.e., with relatively diffuse second-stage priors) both with metric and choice data.