Abstract
Previous results of the application of Lawley's selection theorem to the common factor analysis model are extended to a revision of Tucker's three-mode principal components model. If the regression of the three-mode manifest variates on variates used to select subpopulations is both linear and homoscedastic, the two factor pattern matrices, the core matrix, and the residual variance-covariance matrix in the three-mode model can all be assumed to be invariant across subpopulations. The implication of this finding for simple structure is discussed.
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Bloxom, B. A note on invariance in three-mode factor analysis. Psychometrika 33, 347–350 (1968). https://doi.org/10.1007/BF02289329
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DOI: https://doi.org/10.1007/BF02289329