title: Data-Generating Mechanisms Versus Constructively-Defined Latent Variables in Multitrait-Multimethod Analysis: A Comment on Castro-Schilo, Widaman, and Grimm (2013).
abstract: 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.
authors.affiliation: Department of Psychology, Utah State University.
authors.forename: Christian
authors.initials: C
authors.lastname: Geiser
authors.affiliation: Department of Education and Psychology, Freie Universität Berlin, Germany.
authors.forename: Tobias
authors.initials: T
authors.lastname: Koch
authors.affiliation: Department of Education and Psychology, Freie Universität Berlin, Germany.
authors.forename: Michael
authors.initials: M
authors.lastname: Eid
keywords: CT-C(M – 1) model; CT-CM model; Multitrait-multimethod (MTMM) analysis; constructively-defined latent variables; psychometric theory