Researchers have recently introduced a finite mixture Bayesian regression model to simultaneously identify consumer market segments (heterogeneity) and determine how such segments differ with respect to active regression coefficients (variable selection). This article introduces three extensions of this model to incorporate managerial restrictions (constraints). The authors demonstrate with synthetic data that the new constrained finite mixture Bayesian regression models can be used to identify and represent several constrained heterogeneous response patterns commonly encountered in practice. In addition, they show that the proposed models are more robust against multicollinearity than traditional methods. Finally, to illustrate the proposed models' usefulness, the authors apply the proposed constrained models in the context of a service quality (SERVPERF) survey of National Insurance Company's customers. [ABSTRACT FROM AUTHOR]
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