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A Note on Invariance in Three-Mode Factor Analysis

Author(s):
Bloxom, Bruce
Publication Year:
1967
Report Number:
RB-67-45
Source:
ETS Research Bulletin
Document Type:
Report
Page Count:
6
Subject/Key Words:
Factor Analysis, Invariance Principle, Lawley's Formulas

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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