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A reparameterization of the restricted factor analysis model for multitrait‐multimethod matrices
Author(s) -
Dudgeon Paul
Publication year - 1994
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.2044-8317.1994.tb01038.x
Subject(s) - mathematics , factor (programming language) , econometrics , statistics , computer science , programming language
Some limitations in existing covariance structure models for multitrait multimethod (MTMM) data are discussed as an introduction to a re‐parameterization of the restricted factor analysis model. Unlike existing specifications of this model, the reparameterized model is consistent with Campbell & Fiske's underlying rationale for the MTMM design. It accommodates multiplicative as well as additive relationships in MTMM matrices and provides information concerning the extent to which any matrix conforms to Campbell & Fiske's (1959) four requirements for convergent and discriminant validity. It can also indicate the degree of trait variance in measures that is independent of method effects. Emphasis is placed on the specification of factor correlation matrices which accords with the hypothesized relationships among both traits and methods in an MTMM study. These suggestions are demonstrated by an application of the reparameterized model to an exemplar MTMM matrix which restricted factor analysis has previously found difficult in providing an interpretable solution.