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

Author

Listed:
  • Leila Amiri

    (Shahid Beheshti University)

  • Mojtaba Khazaei

    (Shahid Beheshti University)

  • Mojtaba Ganjali

    (Shahid Beheshti University)

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.

Suggested Citation

  • Leila Amiri & Mojtaba Khazaei & Mojtaba Ganjali, 2017. "General location model with factor analyzer covariance matrix structure and its applications," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 11(3), pages 593-609, September.
    • Handle: RePEc:spr:advdac:v:11:y:2017:i:3:d:10.1007_s11634-016-0258-6
    DOI: 10.1007/s11634-016-0258-6
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    References listed on IDEAS

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    1. Sanjeena Subedi & Antonio Punzo & Salvatore Ingrassia & Paul McNicholas, 2015. "Cluster-weighted $$t$$ t -factor analyzers for robust model-based clustering and dimension reduction," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 24(4), pages 623-649, November.
    2. Sanjeena Subedi & Antonio Punzo & Salvatore Ingrassia & Paul McNicholas, 2013. "Clustering and classification via cluster-weighted factor analyzers," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 7(1), pages 5-40, March.
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