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Sufficient conditions for rotational uniqueness in the additive MTMM model
Author(s) -
Millsap Roger E.
Publication year - 1992
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 - 10.1111/j.2044-8317.1992.tb00981.x
Subject(s) - uniqueness , confirmatory factor analysis , mathematics , statistics , calculus (dental) , mathematical analysis , structural equation modeling , medicine , dentistry
Confirmatory factor analysis is widely used in the analysis of multitrait‐multimethod (MTMM) matrices. Sufficient conditions for rotational uniqueness in the additive MTMM model have not been fully discussed in the literature. A theorem giving sufficient conditions for uniqueness in the additive MTMM model is presented. This theorem reformulates the conditions given by Anderson & Rubin (1956), Howe (1955), and Jöreskog (1979) for the general confirmatory factor analysis model. Several corollaries of the theorem describe special cases of the additive MTMM model that will always be rotationally unique. One of these cases is illustrated with an example using real data. Some implications of these results are discussed.