Confirmatory factor analysis and MTMM matrices

In this paper, second-order factor analysis is compared with a first-order additive model (complete model) traditionally used to analyse convergent an d discriminant validity. A simulation study was performed with the complete model and the second order model as data generators, using multitrait-mult imethod matrices with three traits and three methods. Conditions of the stu dy included several indicators per trait-method combination. Manipulated va riables included sample size (200 and 1000) and correlation among method fa ctors (0..2,.4,.6) and the estimated confirmatory model (complete model and second order model). 100 replications were used in each condition. Depende nt variables under scrutiny were: a)convergence problems, whether or not th e model converged; b) ill-defined solutions; c) bias in the estimation of t rait factor loadings (convergent validity) and trait correlations (discrimi nant validity); and d) the root mean square error in the estimation of the trait factor loadings and trait correlations. Results shown the superiority of the complete model over the second order confirmatory factor analysis. The second order model presented so many estimation problems that almost di scard it as an alternative over the first order models in order to analyse multitrait-multimethod matrices included in this study.