Additive Models for Multitrait–Multimethod Data With a Multiplicative Trait–Method Relationship: A Simulation Study

Abstract

Confirmatory factor analysis (CFA) is widely used for analyzing multitrait-multimethod (MTMM) data. But there is no consensus about whether multiplicative or additive trait-method effect of its parameterization, most appropriately represents the underlying structure of MTMM data. Given the popularity of two additive CFA models, the CT-CM model and the CT-CU model, this simulation investigates their performance for multiplicative MTMM data. Results showed that the CT-CM model had much lower convergence and proper solution rates than the CT-CU model. Although both models had adequate fit for the converged solutions, all parameter estimates from the CT-CM model were unacceptably biased. The CT-CU model worked well in most conditions and was quite robust to the multiplicative data when the matrix size was 3T3M.

Keywords:

• composite direct product model (CDP)
• confirmatory factor analysis (CFA)
• correlated traits-correlated methods model (CT-CM)
• correlated traits-correlated uniqueness model (CT-CU)
• method effects
• multitrait-multimethod (MTMM) analysis