Examining Quadratic Relationships Between Traits and Methods in Two Multitrait-Multimethod Models - Hintz, Fred A.; Geiser, Christian; Burns, G. Leonard; Servera, Mateu (Frontiers in Psychology, 2019)
Psychological researchers are interested in the validity of the measures they use, and the multitrait-multimethod design is one of the most frequently employed methods to examine validity. Confirmatory factor analysis is now a commonly used analytic tool for examining multitrait-multimethod data, where an underlying mathematical model is fit to data and the amount of variance due to the trait and method factors is estimated. While most contemporary confirmatory factor analysis methods for examining multi-trait multi-method data do not allow relationships between the trait and method factors, a few recently proposed models allow for the examination of linear relationships between traits and methods. While these models provide a great advantage in analyzing multitrait-multimethod data, there is no theoretical reason why trait and method relationships should always be linear, and quadratic relationships are frequently proposed in the social sciences. Therefore, this paper proposes and describes in detail two models for examining quadratic relations between traits and methods. An application to a multi-rater study of children with attention deficit and hyperactivity disorder (N=800) and results of a Monte Carlo study to test the applicability of the method under a variety of data conditions are described.