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Generalized data-fitting factor analysis with multiple quantification of categorical variables

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  • Naomichi Makino

Abstract

In this study, a recently proposed data-fitting factor analysis (DFFA) procedure is generalized for categorical variable analysis. For generalized DFFA (GDFFA), we develop an alternating least squares algorithm consisting of a multiple quantification step and a model parameters estimation step. The differences between GDFFA and similar statistical methods such as multiple correspondence analysis and FACTALS are also discussed. The developed algorithm and its solution are illustrated with a real data example. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Naomichi Makino, 2015. "Generalized data-fitting factor analysis with multiple quantification of categorical variables," Computational Statistics, Springer, vol. 30(1), pages 279-292, March.
    • Handle: RePEc:spr:compst:v:30:y:2015:i:1:p:279-292
    DOI: 10.1007/s00180-014-0536-8
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    References listed on IDEAS

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    2. Schneeweiss, H. & Mathes, H., 1995. "Factor Analysis and Principal Components," Journal of Multivariate Analysis, Elsevier, vol. 55(1), pages 105-124, October.
    3. Steffen Unkel & Nickolay T. Trendafilov, 2010. "Simultaneous Parameter Estimation in Exploratory Factor Analysis: An Expository Review," International Statistical Review, International Statistical Institute, vol. 78(3), pages 363-382, December.
    4. Masahiro Kuroda, 2012. "Acceleration of Convergence of the Alternating Least Squares Algorithm for Nonlinear Principal Components Analysis," Chapters, in: Parinya Sanguansat (ed.), Principal Component Analysis, IntechOpen.
    5. Eeke Burg & Jan Leeuw & Renée Verdegaal, 1988. "Homogeneity analysis withk sets of variables: An alternating least squares method with optimal scaling features," Psychometrika, Springer;The Psychometric Society, vol. 53(2), pages 177-197, June.
    6. Michel Tenenhaus & Forrest Young, 1985. "An analysis and synthesis of multiple correspondence analysis, optimal scaling, dual scaling, homogeneity analysis and other methods for quantifying categorical multivariate data," Psychometrika, Springer;The Psychometric Society, vol. 50(1), pages 91-119, March.
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    Cited by:

    1. Kohei Adachi & Nickolay T. Trendafilov, 2018. "Some Mathematical Properties of the Matrix Decomposition Solution in Factor Analysis," Psychometrika, Springer;The Psychometric Society, vol. 83(2), pages 407-424, June.

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