Weighted likelihood latent class linear regression

A weighted likelihood approach for robust fitting of a finite mixture of linear regression models is proposed. An EM type algorithm and its variant based on the classification likelihood have been developed. The proposed algorithm is characterized by an M-step that is enhanced by the computation of weights aimed at downweighting outliers. The weights are based on the Pearson residuals stemming from the assumption of normality for the error distribution. Formal rules for robust clustering and outlier detection are also defined based on the fitted mixture model. The behavior of the proposed methodologies has been investigated by numerical studies and real data examples in terms of both fitting and classification accuracy and outlier detection.