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

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.