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A new method for simultaneous estimation of the factor model parameters, factor scores, and unique parts

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  • Stegeman, Alwin

Abstract

In the common factor model the observed data is conceptually split into a common covariance producing part and an uncorrelated unique part. The common factor model is fitted to the data itself and a new method is introduced for the simultaneous estimation of loadings, unique variances, factor scores, and unique parts. The method is based on Minimum Rank Factor Analysis and allows for the percentage of explained common variance to be computed. Taking into account factor indeterminacy, an explicit description of the complete class of solutions for the factor scores and unique parts is given. The method is evaluated in a simulation study and fitted to a dataset in the literature.

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  • Stegeman, Alwin, 2016. "A new method for simultaneous estimation of the factor model parameters, factor scores, and unique parts," Computational Statistics & Data Analysis, Elsevier, vol. 99(C), pages 189-203.
    • Handle: RePEc:eee:csdana:v:99:y:2016:i:c:p:189-203
    DOI: 10.1016/j.csda.2016.01.012
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    Cited by:

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    2. Kohei Uno & Kohei Adachi & Nickolay T. Trendafilov, 2019. "Clustered Common Factor Exploration in Factor Analysis," Psychometrika, Springer;The Psychometric Society, vol. 84(4), pages 1048-1067, December.
    3. 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.
    4. Kohei Adachi & Nickolay T. Trendafilov, 2018. "Sparsest factor analysis for clustering variables: a matrix decomposition approach," 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. 12(3), pages 559-585, September.

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