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Journal of Classification

08-01-2024

Parsimonious Seemingly Unrelated Contaminated Normal Cluster-Weighted Models

Authors: Gabriele Perrone, Gabriele Soffritti

Published in: Journal of Classification

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Abstract

Normal cluster-weighted models constitute a modern approach to linear regression which simultaneously perform model-based cluster analysis and multivariate linear regression analysis with random quantitative regressors. Robustified models have been recently developed, based on the use of the contaminated normal distribution, which can manage the presence of mildly atypical observations. A more flexible class of contaminated normal linear cluster-weighted models is specified here, in which the researcher is free to use a different vector of regressors for each response. The novel class also includes parsimonious models, where parsimony is attained by imposing suitable constraints on the component-covariance matrices of either the responses or the regressors. Identifiability conditions are illustrated and discussed. An expectation-conditional maximisation algorithm is provided for the maximum likelihood estimation of the model parameters. The effectiveness and usefulness of the proposed models are shown through the analysis of simulated and real datasets.

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Appendix
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Footnotes
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Metadata
Title
Parsimonious Seemingly Unrelated Contaminated Normal Cluster-Weighted Models
Authors
Gabriele Perrone
Gabriele Soffritti
Publication date
08-01-2024
Publisher
Springer US
Published in
Journal of Classification
Print ISSN: 0176-4268
Electronic ISSN: 1432-1343
DOI
https://doi.org/10.1007/s00357-023-09458-8

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