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Some Mathematical Properties of the Matrix Decomposition Solution in Factor Analysis

Adachi, Kohei and Trendafilov, Nickolay (2018). Some Mathematical Properties of the Matrix Decomposition Solution in Factor Analysis. Psychometrika, 83(2) pp. 407–424.

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A new factor analysis (FA) procedure has recently been proposed which can be called matrix decomposition FA (MDFA). All FA model parameters (common and unique factors, loadings, and unique variances) are treated as fixed unknown matrices. Then, the MDFA model simply becomes a specific data matrix decomposition. The MDFA parameters are found by minimizing the discrepancy between the data and the MDFA model. Several algorithms have been developed and some properties have been discussed in the literature (notably by Stegeman in Comput Stat Data Anal 99:189–203, 2016), but, as a whole, MDFA has not been studied fully yet. A number of new properties are discovered in this paper, and some existing ones are derived more explicitly. The properties provided concern the uniqueness of results, covariances among common factors, unique factors, and residuals, and assessment of the degree of indeterminacy of common and unique factor scores. The properties are illustrated using a real data example.

Item Type: Journal Item
Copyright Holders: 2017 The Psychometric Society
ISSN: 1860-0980
Project Funding Details:
Funded Project NameProject IDFunding Body
Not Set(C)- 26330039Japan Society for the Promotion of Science
Keywords: exploratory factor analysis; model identifiability; covariances between factors and residuals; higher rank approximation; factor indeterminacy
Academic Unit/School: Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM)
Item ID: 55018
Depositing User: Nickolay Trendafilov
Date Deposited: 09 May 2018 09:20
Last Modified: 11 Sep 2018 22:11
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