Group-Average and Convex Clustering for Partially Heterogeneous Linear Regression

In this paper, a subgroup least squares and a convex clustering are introduced for inferring a partially heterogenous linear regression that has potential application in the areas of precision marketing and precision medicine. The homogenous parameter and the subgroup-average of the heterogenous parameters can be consistently estimated by the subgroup least squares, without need of the sparsity assumption on the heterogenous parameters. The heterogenous parameters can be consistently clustered via the convex clustering. Unlike the existing methods for regression clustering, our clustering procedure is a standard mean clustering, although the model under study is a type of regression, and the corresponding algorithm only involves low dimensional parameters. Thus, it is simple and stable even if the sample size is large. The advantage of the method is further illustrated via simulation studies and the analysis of car sales data.