Calibrating covariate informed product partition models

Covariate informed product partition models incorporate the intuitively appealing notion that individuals or units with similar covariate values a priori have a higher probability of co-clustering than those with dissimilar covariate values. These methods have been shown to perform well if the number of covariates is relatively small. However, as the number of covariates increase, their influence on partition probabilities overwhelm any information the response may provide in clustering and often encourage partitions with either a large number of singleton clusters or one large cluster resulting in poor model fit and poor out-of-sample prediction. This same phenomenon is observed in Bayesian nonparametric regression methods that induce a conditional distribution for the response given covariates through a joint model. In light of this, we propose two methods that calibrate the covariate-dependent partition model by capping the influence that covariates have on partition probabilities. We demonstrate the new methods’ utility using simulation and two publicly available datasets.