A mathematical programming approach to clusterwise regression model and its extensions

The clusterwise regression model is used to perform cluster analysis within a regression framework. While the traditional regression model assumes the regression coefficient (beta) to be identical for all subjects in the sample, the clusterwise regression model allows beta to vary with subjects of different clusters. Since the cluster membership is unknown, the estimation of the clusterwise regression is a tough combinatorial optimization problem. In this research, we propose a "Generalized Clusterwise Regression Model" which is formulated as a mathematical programming (MP) problem. A nonlinear programming procedure (with linear constraints) is proposed to solve the combinatorial problem and to estimate the cluster membership and beta simultaneously. Moreover, by integrating the cluster analysis with the discriminant analysis, a clusterwise discriminant model is developed to incorporate parameter heterogeneity into the traditional discriminant analysis. The cluster membership and discriminant parameters are estimated simultaneously by another nonlinear programming model. (C) 1999 Elsevier Science B.V. All rights reserved.