Three-mode factor analysis by means of Candecomp/Parafac. (English) Zbl 1308.62127
Summary: 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 \(JK\times JK\) 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.
MSC:
| 62H25 | Factor analysis and principal components; correspondence analysis |
| 62P15 | Applications of statistics to psychology |
Keywords:
three-mode factor analysis; multitrait-multimethod; Candecomp; Parafac; minimum rank factor analysisSoftware:
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