General location model with factor analyzer covariance matrix structure and its applications

General location model with factor analyzer covariance matrix structure and its applications General location model (GLOM) is a well-known model for analyzing mixed data. In GLOM one decomposes the joint distribution of variables into conditional distribution of continuous variables given categorical outcomes and marginal distribution of categorical variables. The first version of GLOM assumes that the covariance matrices of continuous multivariate distributions across cells, which are obtained by different combination of categorical variables, are equal. In this paper, the GLOMs are considered in both cases of equality and unequality of these covariance matrices. Three covariance structures are used across cells: the same factor analyzer, factor analyzer with unequal specific variances matrices (in the general and parsimonious forms) and factor analyzers with common factor loadings. These structures are used for both modeling covariance structure and for reducing the number of parameters. The maximum likelihood estimates of parameters are computed via the EM algorithm. As an application for these models, we investigate the classification of continuous variables within cells. Based on these models, the classification is done for usual as well as for high dimensional data sets. Finally, for showing the applicability of the proposed models for classification, results from analyzing three real data sets are presented. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Advances in Data Analysis and Classification Springer Journals

General location model with factor analyzer covariance matrix structure and its applications

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Publisher
Springer Berlin Heidelberg
Copyright
Copyright © 2016 by Springer-Verlag Berlin Heidelberg
Subject
Statistics; Statistical Theory and Methods; Data Mining and Knowledge Discovery
ISSN
1862-5347
eISSN
1862-5355
D.O.I.
10.1007/s11634-016-0258-6
Publisher site
See Article on Publisher Site

Abstract

General location model (GLOM) is a well-known model for analyzing mixed data. In GLOM one decomposes the joint distribution of variables into conditional distribution of continuous variables given categorical outcomes and marginal distribution of categorical variables. The first version of GLOM assumes that the covariance matrices of continuous multivariate distributions across cells, which are obtained by different combination of categorical variables, are equal. In this paper, the GLOMs are considered in both cases of equality and unequality of these covariance matrices. Three covariance structures are used across cells: the same factor analyzer, factor analyzer with unequal specific variances matrices (in the general and parsimonious forms) and factor analyzers with common factor loadings. These structures are used for both modeling covariance structure and for reducing the number of parameters. The maximum likelihood estimates of parameters are computed via the EM algorithm. As an application for these models, we investigate the classification of continuous variables within cells. Based on these models, the classification is done for usual as well as for high dimensional data sets. Finally, for showing the applicability of the proposed models for classification, results from analyzing three real data sets are presented.

Journal

Advances in Data Analysis and ClassificationSpringer Journals

Published: May 31, 2016

References

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