A Convex Optimization Approach to Modeling Consumer Heterogeneity in Conjoint Estimation

We propose and test a new approach for modeling consumer heterogeneity in conjoint estimation based on convex optimization and statistical machine learning. We develop methods both for metric and choice data. Like hierarchical Bayes (HB), our methods shrink individual-level partworth estimates towards a population mean. However, while HB samples from a posterior distribution that is influenced by exogenous parameters (the parameters of the second-stage priors), we minimize a convex loss function that depends only on endogenous parameters. As a result, the amounts of shrinkage differ between the two approaches, leading to different estimation accuracies. In our comparisons, based on simulations as well as empirical data sets, the new approach overall outperforms standard HB (i.e., with relatively diffuse second-stage priors) both with metric and choice data.