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Stochastic three‐mode models for mean and covariance structures
Author(s) -
Oort Frans J.
Publication year - 1999
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 - 10.1348/000711099159099
Subject(s) - covariance , mode (computer interface) , statistics , interpretation (philosophy) , mathematics , econometrics , analysis of covariance , multivariate statistics , stochastic modelling , terminology , covariance mapping , field (mathematics) , random effects model , covariance function , identification (biology) , computer science , covariance intersection , botany , biology , medicine , linguistics , philosophy , meta analysis , pure mathematics , programming language , operating system
With three‐mode models, the three modes are analysed simultaneously. Examples are the analysis of multitrait‐multimethod data where the modes are traits, methods and subjects, and the analysis of multivariate longitudinal data where the modes are variables, occasions and subjects. If we consider the subjects mode as random, and the other modes as fixed, such data can be analysed using stochastic three‐mode models. Three‐mode factor analysis models and composite direct product models are special cases, but they are models for the covariance structure only. Stochastic three‐mode models for mean and covariance structures are presented, and the identification, estimation and interpretation of the model parameters are discussed. Interpretation is facilitated by introducing a new terminology and by considering various special cases. Analyses of real data from the field of economic psychology serve as an illustration.