{"title":"Parsimonious Seemingly Unrelated Contaminated Normal Cluster-Weighted Models","authors":"","doi":"10.1007/s00357-023-09458-8","DOIUrl":null,"url":null,"abstract":"<h3>Abstract</h3> <p>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.</p>","PeriodicalId":50241,"journal":{"name":"Journal of Classification","volume":"37 1","pages":""},"PeriodicalIF":1.8000,"publicationDate":"2024-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Classification","FirstCategoryId":"94","ListUrlMain":"https://doi.org/10.1007/s00357-023-09458-8","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 0
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.
期刊介绍：
To publish original and valuable papers in the field of classification, numerical taxonomy, multidimensional scaling and other ordination techniques, clustering, tree structures and other network models (with somewhat less emphasis on principal components analysis, factor analysis, and discriminant analysis), as well as associated models and algorithms for fitting them. Articles will support advances in methodology while demonstrating compelling substantive applications. Comprehensive review articles are also acceptable. Contributions will represent disciplines such as statistics, psychology, biology, information retrieval, anthropology, archeology, astronomy, business, chemistry, computer science, economics, engineering, geography, geology, linguistics, marketing, mathematics, medicine, political science, psychiatry, sociology, and soil science.
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