Three-mode analysis of multimode covariance matrices

• Published in: British journal of mathematical & statistical psychology Vol. 56; no. 2; pp. 305 - 335
• Main Authors: Kroonenberg, Pieter M., Oort, Frans J.
• Format: Journal Article
• Language: English
• Published: Oxford, UK Blackwell Publishing Ltd 01.11.2003; British Psychological Society
• Subjects: Analysis of Variance; Humans; Mathematical Computing; Mathematical models; Matrix; Models, Statistical; Psychological Tests - statistics & numerical data; Psychology, Experimental - statistics & numerical data; Psychometrics - statistics & numerical data; Reproducibility of Results; Software; Statistical analysis; Stochastic models; Variance analysis
• ISSN: 0007-1102; 2044-8317
• DOI: 10.1348/000711003770480066

Multimode covariance matrices, such as multitrait‐multimethod matrices, contain the covariances of subject scores on variables for different occasions or conditions. This paper presents a comparison of three‐mode component analysis and three‐mode factor analysis applied to such covariance matrices. The differences and similarities between the non‐stochastic and stochastic approaches are demonstrated by two examples, one of which has a longitudinal design. The empirical comparison is facilitated by deriving, as a heuristic device, a statistic based on the maximum likelihood function for three‐mode factor analysis and its associated degrees of freedom for the three‐mode component models. Furthermore, within the present context a case is made for interpreting the core array as second‐order components.