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Three-Mode Factor Analysis by Means of Candecomp/Parafac

By Alwin Stegeman and Tam T T Lam


<p>A three-mode covariance matrix contains covariances of N observations (e.g., subject scores) on J variables for K different occasions or conditions. We model such an JK×JK covariance matrix as the sum of a (common) covariance matrix having Candecomp/Parafac form, and a diagonal matrix of unique variances. The Candecomp/Parafac form is a generalization of the two-mode case under the assumption of parallel factors. We estimate the unique variances by Minimum Rank Factor Analysis. The factors can be chosen oblique or orthogonal. Our approach yields a model that is easy to estimate and easy to interpret. Moreover, the unique variances, the factor covariance matrix, and the communalities are guaranteed to be proper, a percentage of explained common variance can be obtained for each variable-condition combination, and the estimated model is rotationally unique under mild conditions. We apply our model to several datasets in the literature, and demonstrate our estimation procedure in a simulation study. © 2013 The Psychometric Society.</p>

Topics: Candecomp, minimum rank factor analysis; multitrait-multimethod; Parafac; three-mode factor analysis
Year: 2013
DOI identifier: 10.1007/s11336-013-9359-8
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