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Identification with Deficient Rank Loading Matrices in Confirmatory Factor Analysis: Multitrait-Multimethod Models

Published online by Cambridge University Press:  01 January 2025

David Grayson  and
Herbert W. Marsh
David Grayson*
Affiliation:
University of Sydney
Herbert W. Marsh
Affiliation:
University of Western Sydney
*
Requests for reprints should be sent to D. A. Grayson, Aged and Extended Care Department, C25, Concord Hospital, NSW 2139, AUSTRALIA
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Abstract

This paper presents some results on identification in multitrait-multimethod (MTMM) confirmatory factor analysis (CFA) models. Some MTMM models are not identified when the (factorial-patterned) loadings matrix is of deficient column rank. For at least one other MTMM model, identification does exist despite such deficiency. It is also shown that for some MTMM CFA models, Howe's (1955) conditions sufficient for rotational uniqueness can fail, yet the model may well be identified and rotationally unique. Implications of these results for CFA models in general are discussed.

Keywords

multitrait-multimethodidentificationrank conditionconfirmatory factor analysisrotational uniqueness
Type
Article
Information
Psychometrika , Volume 59 , Issue 1 , March 1994 , pp. 121 - 134
Copyright
Copyright © 1994 The Psychometric Society

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