مدل سازی رگرسیون خطی خوشه ای با محدودیت های مقیاس نرم

Constrained approaches to maximum likelihood estimation in the context of finite mixtures of normals have been presented in the literature. A fully data-dependent soft constrained method for maximum likelihood estimation of clusterwise linear regression is proposed, which extends previous work in equivariant data-driven estimation of finite mixtures of normals. The method imposes soft scale bounds based on the homoscedastic variance and a cross-validated tuning parameter c. In our simulation studies and real data examples we show that the selected c will produce an output model with clusterwise linear regressions and clustering as a most-suited-to-the-data solution in between the homoscedastic and the heteroscedastic models.