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Three‐mode analysis of multimode covariance matrices
Author(s) -
Kroonenberg Pieter M.,
Oort Frans J.
Publication year - 2003
Publication title -
british journal of mathematical and statistical psychology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.157
H-Index - 51
eISSN - 2044-8317
pISSN - 0007-1102
DOI - 10.1348/000711003770480066
Subject(s) - covariance , statistic , mathematics , covariance matrix , context (archaeology) , mode (computer interface) , analysis of covariance , covariance function , covariance mapping , degrees of freedom (physics and chemistry) , heuristic , statistics , computer science , mathematical optimization , covariance intersection , paleontology , physics , quantum mechanics , biology , operating system
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.