ABSTRACT
A most important contribution to the study of construct validity was the proposal of the multitrait-multimethod (MTMM) matrix by Campbell and Fiske in 1959. During the past half-century, three principal confirmatory factor analysis (CFA) models have been used to represent relations among variables in an MTMM. Each of the three models includes one latent variable for each of the multiple trait constructs in the MTMM, allowing correlations among these trait factors. The models differ in how they represent method effects. The three models are: (a) the correlated trait-correlated method, or CT-CM, model, which contains one method factor for each of the methods in the MTMM, allowing correlations among the method factors; (b) the correlated trait-correlated method-minus-one, or CT-C(M-1), model, which deletes one of the method factors; and (c ) the correlated trait-correlated uniqueness, or CT-CU, model, which substitutes covariances among unique factors for indicators for a common method in place of method factors. Each of these models has its own theoretical basis, with attendant strengths and weaknesses. Likewise, each model has strengths and weaknesses in the empirical realm, when fitting models to data. The primary aim of this chapter was to compare and contrast the three CFA models with regard to their theoretical and empirical qualities. One empirical example was employed to contrast findings across the models. For this one empirical example, the CT-CM model had very good fit to the data, and the CT-C(M-1) and CT-CU models has less adequate fit. But, this was just a single empirical data set, and other models might provide superior fit to other sets of empirical data. When we fit models to data, we cannot be sure which model will automatically provide best fit, but we trust that models and their fit will inform us about the processes under study. No one should promote only a single model in dogmatic fashion. Instead, researchers should be encouraged to fit alternative models and then to cross-validate the model that provides optimal fit for a given empirical context.
