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. 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.