Three-Mode Models for Multitrait-Multimethod Data

Multitrait-multimethod (MTMM) data are characterized by three modes: traits, methods, and subjects. Considering subjects as random, and traits and methods as fixed, stochastic three-mode models can be used to analyze MTMM covariance data. Stochastic three-mode models can be written as linear latent variable models with direct product (DP) restrictions on the parameter matrices (Oort, 1999), yielding three-mode factor models (Bentler & Lee, 1979) and composite direct product models (Browne, 1984) as special cases. DP restrictions on factor loadings and factor correlations facilitate interpretation of the results and enable easy evaluation of the validity requirements of MTMM correlations (Campbell & Fiske, 1959). As an illustrative example, a series of stochastic three-mode models has been fitted to data of three personality traits of 482 students, measured with 12 items, through three methods.