Multi‐set factor analysis by means of Parafac2. (3rd November 2015)

• Record Type: Journal Article
• Authors: Stegeman, Alwin; Lam, Tam T. T.
• Is Part Of: British journal of mathematical & statistical psychology. Volume 69:Part 1(2016:Feb.)
• Page Start: 1
• Page End: 19
• Publication Date: 2015-11-03
• Subjects: multi‐set data -- factor analysis -- Parafac -- Parafac2 -- minimum rank factor analysis; Psychometrics -- Periodicals; Psychology -- Mathematical models -- Periodicals; Psychology -- Statistical methods -- Periodicals; 150.727
• DOI: 10.1111/bmsp.12061
• Languages: English
• ISSNs: 0007-1102

Abstract

Abstract : We consider multi‐set data consisting of N k observations, k = 1, …, K (e.g., subject scores), on J variables in K different samples. We introduce a factor model for the J × J covariance matrices Σ k, k = 1, …, K, where the common part is modelled by Parafac2 and the unique variances U k, k = 1, …, K, are diagonal. The Parafac2 model implies a common loadings matrix that is rescaled for each k, and a common factor correlation matrix. We estimate the unique variances U k by minimum rank factor analysis on Σ k for each k . The factors can be chosen orthogonal or oblique. We present a novel algorithm to estimate the Parafac2 part and demonstrate its performance in a simulation study. Also, we fit our model to a data set in the literature. Our model is easy to estimate and interpret. The unique variances, the factor correlation matrix and the communalities are guaranteed to be proper, and a percentage of explained common variance can be computed for each k . Also, the Parafac2 part is rotationally unique under mild conditions.