On the Correlation of Common Factors with Variance Not Accounted for by the Factor Model. Issue 6 (2nd July 2016)

• Record Type: Journal Article
• Authors: Beauducel, André; Hilger, Norbert
• Is Part Of: Communications in statistics. Volume 45:Issue 6(2016)
• Page Start: 2145
• Page End: 2157
• Publication Date: 2016-07-02
• Subjects: Factor analysis -- Factor score predictor -- Principal component analysis; MSC2010 -- 62H25; Mathematical statistics -- Periodicals; Mathematical statistics -- Data processing -- Periodicals; Digital computer simulation -- Periodicals; 519.5
• DOI: 10.1080/03610918.2014.890223
• Languages: English
• ISSNs: 0361-0918

Abstract

Abstract : The case that the factor model does not account for all the covariances of the observed variables is considered. It is shown that principal components representing covariances not accounted for by the factor model can have a nonzero correlation with the common factors of the factor model. The substantial correlations of components representing variance not accounted for by the factor model with common factors are demonstrated in a simulation study comprising model error. Based on these results, a new version of Harman's factor score predictor minimizing the correlation with residual components is proposed.