A new OLS-based procedure for clusterwise linear regression
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Data heterogeneity, within a (linear) regression framework, often suggest the use of a Clusterwise
Linear Regression (CLR) procedure, which implies, among other things, the estimate of the appropriate
number of clusters as well as the cluster membership of each unit. The approaches to the estimation
of a CLR model are essentially based on the Ordinary Least Square (OLS) criterion or the
likelihood criterion. In this paper, in a context of OLS approach, we propose an estimation of the
model making use of an algorithm based on a threshold criterion for the determination coefficient
of each cluster, to identify the appropriate number of clusters, and of a modified Spath’s algorithm,
to estimate the cluster membership of each sample unit. A simulation design and an application to
a real data-set show that the procedure outperforms other algorithms commonly used in literature.
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