Three-mode analysis of multimode covariance matrices
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....
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| Published in | British journal of mathematical & statistical psychology Vol. 56; no. 2; pp. 305 - 335 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Oxford, UK
Blackwell Publishing Ltd
01.11.2003
British Psychological Society |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0007-1102 2044-8317 |
| DOI | 10.1348/000711003770480066 |
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| Abstract | 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. |
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| AbstractList | 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. References: 27 references open in new window Articles that cite this article? 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. 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. [PUBLICATION ABSTRACT] 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.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. |
| Author | Kroonenberg, Pieter M. Oort, Frans J. |
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| BackLink | https://www.ncbi.nlm.nih.gov/pubmed/14633338$$D View this record in MEDLINE/PubMed |
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| Copyright | 2003 The British Psychological Society Copyright British Psychological Society Nov 2003 |
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| Snippet | Multimode covariance matrices, such as multitrait‐multimethod matrices, contain the covariances of subject scores on variables for different occasions or... Multimode covariance matrices, such as multitrait-multimethod matrices, contain the covariances of subject scores on variables for different occasions or... |
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| SubjectTerms | 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 |
| Title | Three-mode analysis of multimode covariance matrices |
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