IDENTIFICATION WITH DEFICIENT RANK LOADING MATRICES IN CONFIRMATORY FACTOR-ANALYSIS - MULTITRAIT-MULTIMETHOD MODELS

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