Assessing factorial invariance of two-way rating designs using three-way methods

Abstract

Assessing the factorial invariance of two-way rating designs such as ratings of concepts on several scales by different groups can be carried out with three-way models such as the Parafac and Tucker models. By their definitions these models are double-metric factorially invariant. The differences between these models lie in their handling of the links between the concept and scale spaces. These links may consist of unrestricted linking (Tucker2 model), invariant component covariances but variable variances per group and per component (Parafac model), zero covariances and variances different per group but not per component (Replicated Tucker3 model) and strict invariance (Component analysis on the average matrix). This hierarchy of invariant models, and the procedures by which to evaluate the models against each other, is illustrated in some detail with an international data set from attachment theory.

Editorial: Measurement Invariance

“…Albeit being analyzed differently, a comparable design to the MTMM is the two-way rating design utilized in situations where subjects have to judge to what extent a particular scale or variable pertains to a particular concept or situation. Kroonenberg ( 2014 ) presents an approach applicable to the assessment of MI in two-way rating designs. In his approach, a hierarchy of models is proposed, each one conceptualizing a form of MI, varying in terms of strictness.…”