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.