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Model‐related factor score predictors for confirmatory factor analysis
Author(s) -
Beauducel André,
Rabe Sirko
Publication year - 2009
Publication title -
british journal of mathematical and statistical psychology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.157
H-Index - 51
eISSN - 2044-8317
pISSN - 0007-1102
DOI - 10.1348/000711008x336146
Subject(s) - confirmatory factor analysis , factor analysis , factor regression model , regression , statistics , mathematics , factor (programming language) , regression analysis , covariance , rotation matrix , structural equation modeling , computer science , polynomial regression , geometry , proper linear model , programming language
The present paper introduces model‐related (MR) factor score predictors, which reflect specific aspects of confirmatory factor models. The development is mainly based on Schönemann and Steiger's regression score components, but it can also be applied to the factor score coefficients. It is shown that the rotation of factor score predictors has no impact on the covariance matrix reproduced from the corresponding regression component patterns. Thus, regression score components or factor score coefficients can be rotated in order to obtain the required properties. This idea is the basis for MR factor score predictors, which are computed by means of a partial Procrustes rotation towards a target pattern representing the interesting properties of a confirmatory factor model. Two examples demonstrate the construction of MR factor score predictors reflecting specific constraints of a factor model.