Graphical and Computational Tools to Guide Parameter Choice for the Cluster Weighted Robust Model

The Cluster Weighted Robust Model (CWRM) is a recently introduced methodology to robustly estimate mixtures of regressions with random covariates. The CWRM allows users to flexibly perform regression clustering, safeguarding it against data contamination and spurious solutions. Nonetheless, the resu...

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Bibliographic Details
Published inJournal of computational and graphical statistics Vol. 32; no. 3; pp. 1195 - 1214
Main Authors Cappozzo, Andrea, García-Escudero, Luis Angel, Greselin, Francesca, Mayo-Iscar, Agustín
Format Journal Article
LanguageEnglish
Published Alexandria Taylor & Francis 03.07.2023
Taylor & Francis Ltd
Subjects
Cluster-weighted modeling
Clustering
Eigenvalue constraint
Mixtures
Model-based clustering
Monitoring
Optimization
Outliers
Robust estimation
Software
Stability analysis
Trimmed BIC
Trimming
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Summary:The Cluster Weighted Robust Model (CWRM) is a recently introduced methodology to robustly estimate mixtures of regressions with random covariates. The CWRM allows users to flexibly perform regression clustering, safeguarding it against data contamination and spurious solutions. Nonetheless, the resulting solution depends on the chosen number of components in the mixture, the percentage of impartial trimming, the degree of heteroscedasticity of the errors around the regression lines and of the clusters in the explanatory variables. Therefore, an appropriate model selection is crucially required. Such a complex modeling task may generate several "legitimate" solutions: each one derived from a distinct hyperparameters specification. The present article introduces a two step-monitoring procedure to help users effectively explore such a vast model space. The first phase uncovers the most appropriate percentages of trimming, whilst the second phase explores the whole set of solutions, conditioning on the outcome derived from the previous step. The final output singles out a set of "top" solutions, whose optimality, stability and validity is assessed. Novel graphical and computational tools-specifically tailored for the CWRM framework-will help the user make an educated choice among the optimal solutions. Three examples on real datasets showcase our proposal in action. Supplementary files for this article are available online.
ISSN:1061-8600
1537-2715
DOI:10.1080/10618600.2022.2154218