Constrained maximum likelihood estimation of clusterwise linear regression models with unknown number of components

TL;DR

This paper introduces a data-driven, constrained maximum likelihood approach for clusterwise linear regression models that effectively determines the number of components and improves estimation accuracy while reducing computational time.

Contribution

It proposes an equivariant, variance-bounding method with a computational shortcut for model selection and parameter estimation in clusterwise linear regression.

Findings

Reliable assessment of the number of components

Accurate model parameter estimation

Reduced computational time

Abstract

We consider an equivariant approach imposing data-driven bounds for the variances to avoid singular and spurious solutions in maximum likelihood (ML) estimation of clusterwise linear regression models. We investigate its use in the choice of the number of components and we propose a computational shortcut, which significantly reduces the computational time needed to tune the bounds on the data. In the simulation study and the two real-data applications, we show that the proposed methods guarantee a reliable assessment of the number of components compared to standard unconstrained methods, together with accurate model parameters estimation and cluster recovery.