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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.