(1996) examined the extent to which children’s self-reports of their depression were concordant with the reports of their parents, their teachers, and their peers, thus testing convergent validity. 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). 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). Convergent and discriminant validity are two aspects of validity that researchers typically study ( American Educational Research Association et al., 2014). In psychology, researchers frequently examine the validity of tests and measurements they use. 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. 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). There is no theoretical reason why trait and method relationships should always be linear, and quadratic relationships are frequently proposed in the social sciences.
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. Confirmatory factor analysis (CFA) is a commonly used analytic tool for examining MTMM data through the specification of trait and method latent variables. Multitrait-multimethod (MTMM) analysis is one of the most frequently employed methods to examine the validity of psychological measures.