Penalized Versus Constrained Approaches for Clusterwise Linear Regression Modeling

Several approaches exist to avoid singular and spurious solutions in maximum likelihood (ML) estimation of clusterwise linear regression models. We propose to solve the degeneracy problem by using a penalized approach: this is done by adding a penalty term to the log-likelihood function which increasingly penalizes smaller values of the scale parameters, and the tuning of the penalty term is done based on the data. Another traditional solution to degeneracy consists in imposing constraints on the variances of the regression error terms (constrained approach). We will compare the penalized approach to the constrained approach in a simulation study, providing practical guidelines on which approach to use under different circumstances.