AUTHOR=Kroonenberg Pieter M. 

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

JOURNAL=Frontiers in Psychology

VOLUME=Volume 5 - 2014

YEAR=2015

URL=https://www.frontiersin.org/journals/psychology/articles/10.3389/fpsyg.2014.01495

DOI=10.3389/fpsyg.2014.01495

ISSN=1664-1078

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. Differences between these models are contained 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 (Principal component analysis on the average matrix). This hierarchy of invariant models and procedures to evaluate the models against each other, is illustrated in some detail with an international data set from attachment theory.