A Cross-Classified CFA-MTMM Model for Structurally Different and Nonindependent Interchangeable Methods

Multirater (multimethod, multisource) studies are increasingly applied in psychology. Eid and colleagues (2008) proposed a multilevel confirmatory factor model for multitrait-multimethod (MTMM) data combining structurally different and multiple independent interchangeable methods (raters). In many studies, however, different interchangeable raters (e.g., peers, subordinates) are asked to rate different targets (students, supervisors), leading to violations of the independence assumption and to cross-classified data structures. In the present work, we extend the ML-CFA-MTMM model by Eid and colleagues (2008) to cross-classified multirater designs. The new C4 model (Cross-Classified CTC[M-1] Combination of Methods) accounts for nonindependent interchangeable raters and enables researchers to explicitly model the interaction between targets and raters as a latent variable. Using a real data application, it is shown how credibility intervals of model parameters and different variance components can be obtained using Bayesian estimation techniques.