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A Model Implied Instrumental Variable Approach to Exploratory Factor Analysis (MIIV-EFA)

Published online by Cambridge University Press:  27 December 2024

Kenneth A. Bollen Open the ORCID record for Kenneth A. Bollen [Opens in a new window] ,
Kathleen M. Gates  and
Lan Luo
Kenneth A. Bollen*
Affiliation:
University of North Carolina at Chapel Hill
Kathleen M. Gates
Affiliation:
University of North Carolina at Chapel Hill
Lan Luo
Affiliation:
University of North Carolina at Chapel Hill
*
Correspondence should bemade to Kenneth A. Bollen, Thurstone Psychometric Laboratory, Department of Psychology and Neuroscience, Department of Sociology, University of North Carolina at Chapel Hill, 235 E. Cameron Avenue, Chapel Hill, NC 27599-3270, USA. Email: bollen@unc.edu
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Abstract

Spearman (Am J Psychol 15(1):201–293, 1904. https://doi.org/10.2307/1412107) marks the birth of factor analysis. Many articles and books have extended his landmark paper in permitting multiple factors and determining the number of factors, developing ideas about simple structure and factor rotation, and distinguishing between confirmatory and exploratory factor analysis (CFA and EFA). We propose a new model implied instrumental variable (MIIV) approach to EFA that allows intercepts for the measurement equations, correlated common factors, correlated errors, standard errors of factor loadings and measurement intercepts, overidentification tests of equations, and a procedure for determining the number of factors. We also permit simpler structures by removing nonsignificant loadings. Simulations of factor analysis models with and without cross-loadings demonstrate the impressive performance of the MIIV-EFA procedure in recovering the correct number of factors and in recovering the primary and secondary loadings. For example, in nearly all replications MIIV-EFA finds the correct number of factors when N is 100 or more. Even the primary and secondary loadings of the most complex models were recovered when the sample sizes were at least 500. We discuss limitations and future research areas. Two appendices describe alternative MIIV-EFA algorithms and the sensitivity of the algorithm to cross-loadings.

Keywords

exploratory factor analysislatent variablesmodel implied instrumental variablesmiivnumber of factorsexploratory analysis
Type
Theory & Methods
Information
Psychometrika , Volume 89 , Issue 2 , June 2024 , pp. 687 - 716
Copyright
Copyright © 2024 The Author(s), under exclusive licence to The Psychometric Society

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Footnotes

Supplementary Information The online version contains supplementary material available at https://doi.org/10.1007/s11336-024-09949-6.

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