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Rotating Factors to Simplify Their Structural Paths

Published online by Cambridge University Press:  01 January 2025

Guangjian Zhang Open the ORCID record for Guangjian Zhang [Opens in a new window] ,
Minami Hattori  and
Lauren A. Trichtinger
Guangjian Zhang*
Affiliation:
University of Notre Dame
Minami Hattori
Affiliation:
Soka University
Lauren A. Trichtinger
Affiliation:
Simmons University
*
Correspondence should be made to Guangjian Zhang, Psychology Department, University of Notre Dame, 390 Corbett Family Hall, Notre Dame, IN 46556, USA. Email: [email protected]
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Abstract

Applications of structural equation modeling (SEM) may encounter issues like inadmissible parameter estimates, nonconvergence, or unsatisfactory model fit. We propose a new factor rotation method that reparameterizes the factor correlation matrix in exploratory factor analysis (EFA) such that factors can be either exogenous or endogenous. The proposed method is an oblique rotation method for EFA, but it allows directional structural paths among factors. We thus referred it to as FSP (factor structural paths) rotation. In particular, we can use FSP rotation to “translate” an SEM model to incorporate theoretical expectations on both factor loadings and structural parameters. We illustrate FSP rotation with an empirical example and explore its statistical properties with simulated data. The results include that (1) EFA with FSP rotation tends to fit data better and encounters fewer Heywood cases than SEM does when there are cross-loadings and many small nonzero loadings, (2) FSP rotated parameter estimates are satisfactory for small models, and (3) FSP rotated parameter estimates are more satisfactory for large models when the structural parameter matrices are sparse.

Keywords

structural equation modelingSEMfactor analysisEFAfactor rotationoblique rotation
Type
Theory & Methods
Information
Psychometrika , Volume 88 , Issue 3 , September 2023 , pp. 865 - 887
Copyright
Copyright © 2022 The Author(s) under exclusive licence to The Psychometric Society

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