Neglect the Structure of Multitrait-Multimethod Data at Your Peril: Implications for Associations With External Variables

In 1959, Campbell and Fiske introduced the use of multitrait–multimethod (MTMM) matrices in psychology, and for the past 4 decades confirmatory factor analysis (CFA) has commonly been used to analyze MTMM data. However, researchers do not always fit CFA models when MTMM data are available; when CFA modeling is used, multiple models are available that have attendant strengths and weaknesses. In this article, we used a Monte Carlo simulation to investigate the drawbacks of either using CFA models that fail to match the data-generating model or completely ignore the MTMM structure of data when the research goal is to uncover associations between trait constructs and external variables. We then used data from the National Institute of Child Health and Human Development Study of Early Child Care and Youth Development to illustrate the substantive implications of fitting models that partially or completely ignore MTMM data structures. Results from analyses of both simulated and empirical data show noticeable biases when the MTMM data structure is partially or completely neglected.     

Toward Improving the Modeling of MTMM Data: A Response to Geiser,Koch, and Eid (2014)

Geiser, Koch, and Eid (2014) expressed their views on an article we published describing findings from a simulation study and an empirical study of multitrait–multimethod (MTMM) data. Geiser and colleagues raised concerns with (a) our use of the term bias, (b) our statement that the correlated trait–correlated method minus one [CT–C(M–1)] model is not in line with Campbell and Fiske’s (1959) conceptualization of MTMM data, (c) our selection of a data-generating model for our simulation study, and (d) our preference for the correlated trait–correlated method (CT–CM) model over the CT–C(M–1) model. Here, we respond to and elaborate on issues raised by Geiser et al. We maintain our position on each of these issues and point to the interpretational challenges of the CT–C(M–1) model. But, we clarify our opinion that none of the existing structural models for MTMM data are flawless; each has its strengths and each has its weaknesses. We further remind readers of the goal, findings, and implications of our recently published article.     

Residual Structures in Growth Models With Ordinal Outcomes

Growth models allow for the study of within-person change and between-person differences in within-person change. Typically, these models are applied to continuous variables where the residuals are assumed to be normally distributed. With normally distributed residuals there are a variety of residual structures that can be imposed and tested, which have been shown to affect model fit and parameter estimation. This article concerns residual structures in growth models with binary and ordered categorical outcomes using the probit link function. Different residual structures and their appropriateness for growth data are discussed and their use is illustrated with longitudinal data collected as part of Head Start’s Family and Child Experiences Survey 1997 Cohort. We close with recommendations for the specification and parameterization of growth models that use the probit link.     

Augmenting the Correlated Trait–Correlated Method Model for Multitrait–Multimethod Data

We introduce an approach for ensuring empirical identification of the correlated trait–correlated method (CT–CM) model under a variety of conditions. A set of models are referred to as augmented correlated trait–correlated method (ACT–CM) models because they are based on systematically augmenting the multitrait–multimethod matrix put forth by Campbell and Fiske (1959). We show results from a Monte Carlo simulation study in which data characteristics lead to an empirically underidentified standard CT–CM model, but a well-identified fully augmented correlated trait–correlated method (FACT–CM) model. This improved identification occurs even for a model in which equality constraints are imposed on loadings on each trait factor and loadings on each method factor—a specific case shown to lead to an empirically underidentified CT–CM model.