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Mixtures of common factor analyzers for high-dimensional data with missing information

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  • Wang, Wan-Lun

Abstract

Mixtures of common factor analyzers (MCFA), thought of as a parsimonious extension of mixture factor analyzers (MFA), have recently been developed as a novel approach to analyzing high-dimensional data, where the number of observations n is not very large relative to their dimension p. The key idea behind MCFA is to reduce further the number of parameters in the specification of the component-covariance matrices. An attractive and important feature of MCFA is to allow visualizing data in lower dimensions. The occurrence of missing data persists in many scientific investigations and often complicates data analysis. In this paper, we establish a computationally flexible EM-type algorithm for parameter estimation of the MCFA model with partially observed data. To facilitate the implementation, two auxiliary permutation matrices are incorporated into the estimating procedure for exactly extracting the location of observed and missing components of each observation. Practical issues related to the specification of initial values, model-based clustering and discriminant procedure are also discussed. Our methodology is illustrated through real and simulated examples.

Suggested Citation

  • Wang, Wan-Lun, 2013. "Mixtures of common factor analyzers for high-dimensional data with missing information," Journal of Multivariate Analysis, Elsevier, vol. 117(C), pages 120-133.
    • Handle: RePEc:eee:jmvana:v:117:y:2013:i:c:p:120-133
    DOI: 10.1016/j.jmva.2013.02.003
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    Cited by:

    1. Zhao, Jianhua & Shi, Lei, 2014. "Automated learning of factor analysis with complete and incomplete data," Computational Statistics & Data Analysis, Elsevier, vol. 72(C), pages 205-218.
    2. Wan-Lun Wang & Luis M. Castro & Yen-Ting Chang & Tsung-I Lin, 2019. "Mixtures of restricted skew-t factor analyzers with common factor loadings," 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. 13(2), pages 445-480, June.
    3. Lin, Tsung-I & McLachlan, Geoffrey J. & Lee, Sharon X., 2016. "Extending mixtures of factor models using the restricted multivariate skew-normal distribution," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 398-413.
    4. Wang, Wan-Lun, 2015. "Mixtures of common t-factor analyzers for modeling high-dimensional data with missing values," Computational Statistics & Data Analysis, Elsevier, vol. 83(C), pages 223-235.
    5. O’Hagan, Adrian & Murphy, Thomas Brendan & Gormley, Isobel Claire & McNicholas, Paul D. & Karlis, Dimitris, 2016. "Clustering with the multivariate normal inverse Gaussian distribution," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 18-30.
    6. Wan-Lun Wang & Tsung-I Lin, 2017. "Flexible clustering via extended mixtures of common t-factor analyzers," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 101(3), pages 227-252, July.

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