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CFA Models with a General Factor and Multiple Sets of Secondary Factors

Published online by Cambridge University Press:  01 January 2025

Minjeong Jeon ,
Frank Rijmen  and
Sophia Rabe-Hesketh
Minjeong Jeon*
Affiliation:
University of California, Los Angeles
Frank Rijmen
Affiliation:
American Institutes for Research
Sophia Rabe-Hesketh
Affiliation:
University of California, Berkeley
*
Correspondence should be made to Minjeong Jeon, Department of Education, University of California, Los Angeles, 457 Portola Plaza, Los Angeles, CA 90095, USA. Email: mjjeon@ucla.edu
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Abstract

We propose a class of confirmatory factor analysis models that include multiple sets of secondary or specific factors and a general factor. The general factor accounts for the common variance among manifest variables, whereas multiple sets of secondary factors account for the remaining source-specific dependency among subsets of manifest variables. A special case of the model is further proposed which constrains the specific factor loadings to be proportional to the general factor loadings. This proportional model substantially reduces the number of model parameters while preserving the essential structure of the general model. Furthermore, the proportional model allows for the interpretation of latent variables as the expected values of the observed manifest variables, decomposition of the variances, and the inclusion of interactions, similar to generalizability theory. We provide two applications to illustrate the utility of the proposed class of models.

Keywords

multifacet modelsbifactor modelstrifactor modelsproportional modelssecondary variance sourcesgeneral factorvariance decompositiongeneralizability theory
Type
Original Paper
Information
Psychometrika , Volume 83 , Issue 4 , December 2018 , pp. 785 - 808
Copyright
Copyright © 2018 The Psychometric Society

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