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Clusterwise linear regression modeling with soft scale constraints
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DOI：10.1016/j.ijar.2017.09.006.png)
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Abstract
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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. (C) 2017 Elsevier Inc. All rights reserved.
Keywords:
Clusterwise linear regression
Adaptive constraints
Regression equivariance
Plausible bounds
Soft estimators
Constrained EM algorithm
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