Examining Quadratic Relationships Between Traits and Methods in Two Multitrait-Multimethod Models.

Fred A Hintz,Christian Geiser,G Leonard Burns,Mateu Servera

doi:10.3389/fpsyg.2019.00353

Abstract

Multitrait-multimethod (MTMM) analysis is one of the most frequently employed methods to examine the validity of psychological measures. Confirmatory factor analysis (CFA) is a commonly used analytic tool for examining MTMM data through the specification of trait and method latent variables. Most contemporary CFA-MTMM models either do not allow estimating correlations between the trait and method factors or they are restricted to linear trait-method relationships. There is no theoretical reason why trait and method relationships should always be linear, and quadratic relationships are frequently proposed in the social sciences. In this article, we present two approaches for examining quadratic relations between traits and methods through extended latent difference and latent means CFA-MTMM models (Pohl et al., 2008; Pohl and Steyer, 2010). An application of the new approaches to a multi-rater study of the nine inattention symptoms of attention-deficit/hyperactivity disorder in children (N = 752) and the results of a Monte Carlo study to test the applicability of the models under a variety of data conditions are described.

Highlights

In psychology, researchers frequently examine the validity of tests and measurements they use
Model fit is identical for the linear latent difference (LD) and latent means (LM) models for a given set of data, the means and variances of the trait and method factors as well as the size and direction of the trait-method relationship can be very different in each model (In Appendix A, we provide more formal details on how each of the structural parameters of the LD and LM models can be derived from the baseline trait-method unit (TMU) model)
We present extensions to the LD and LM models that allow for an examination of quadratic trait-method relationships

Summary

Introduction

Researchers frequently examine the validity of tests and measurements they use. Evidence for convergent validity is provided when different measures (or “methods of measurement”) of the same psychological construct are strongly related (Cronbach and Meehl, 1955; Campbell and Fiske, 1959). Evidence for discriminant validity is provided when measures of different constructs (that pertain to the same or different methods) are sufficiently distinct from each other (Campbell and Fiske, 1959). The authors examined discriminant validity by looking at the extent to which the relations between the ratings of child depression, academic competence, and social competence were inflated due to the use of the same reporter type

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Results

Discussion

Conclusion