Monitoring Hyperparameter Choice for Robust Cluster Weighted Model

The estimation of the ClusterWeighted Model is particularly attractive for providing explicit modeling of the explanatory variables, in a mixture of regression. The Robust version of the model requires the specification of a set of crucial parameters, like the proportion of trimmed units U, the thresholds to be adopted for the constrained estimation of group scatter and for regression errors, beyond the number of components of the Mixture. To assist the choice of such hyper-parameters, a monitoring methodology could be of great help. The purpose is to provide a set of graphical tools to guide the final user in making an informed judgment, considering a landscape of plausible choices. The final output offers a set of optimal solutions, featured by the interval of hyper-parameters values in which their optimality holds, their stability and validity. An assessment of the role and extent of the outlying observations has been provided, introducing three new silhouette plots. The purpose is to understand the possible effects of the contaminated observations, with respect to the clustering of the covariate -, and the local regression lines, following the nature of the Cluster Weighted model.