Data-Generating Mechanisms Versus Constructively-Defined Latent Variables in Multitrait-Multimethod Analysis: A Comment on Castro-Schilo, Widaman, and Grimm (2013).

In a recent article, Castro-Schilo, Widaman, and Grimm (2013) compared different approaches for relating multitrait-multimethod (MTMM) data to external variables. Castro-Schilo et al. reported that estimated associations with external variables were in part biased when either the Correlated Traits-Correlated Uniqueness (CT-CU) or Correlated Traits-Correlated (Methods - 1) [CT-C(M - 1)] models were fit to data generated from the Correlated Traits-Correlated Methods (CT-CM) model, whereas the data-generating CT-CM model accurately reproduced these associations. Castro-Schilo et al. argued that the CT-CM model adequately represents the data-generating mechanism in MTMM studies, whereas the CT-CU and CT-C(M - 1) models do not fully represent the MTMM structure. In this comment, we question whether the CT-CM model is more plausible as a data-generating model for MTMM data than the CT-C(M - 1) model. We show that the CT-C(M - 1) model can be formulated as a reparameterization of a basic MTMM true score model that leads to a meaningful and parsimonious representation of MTMM data. We advocate the use CFA-MTMM models in which latent trait, method, and error variables are explicitly and constructively defined based on psychometric theory.