title: Three-mode factor analysis by means of Candecomp/Parafac.
abstract: 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.
authors.affiliation: Heymans Institute for Psychological Research, University of Groningen, Grote Kruisstraat 2/1, 9712 TS, Groningen, The Netherlands, a.w.stegeman@rug.nl.
authors.forename: Alwin
authors.initials: A
authors.lastname: Stegeman
authors.forename: Tam T T
authors.initials: TT
authors.lastname: Lam
mesh_terms: D005163:Factor Analysis, Statistical; D006801:Humans; D015233:Models, Statistical; D010551:Personality; D011594:Psychometrics / Q000379:methods*