Kroonenberg Pieter M
Department of Child and Family Studies, Institute of Education and Child Studies, Leiden University Leiden, The Netherlands.
Front Psychol. 2015 Jan 8;5:1495. doi: 10.3389/fpsyg.2014.01495. eCollection 2014.
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.
评估双向评级设计（如不同群体在多个量表上对概念进行评级）的因子不变性，可以使用三向模型（如平行因子分析模型和塔克模型）来进行。根据其定义，这些模型在因子方面是双度量不变的。这些模型之间的差异在于它们对概念空间和量表空间之间联系的处理方式。这些联系可能包括无限制链接（塔克2模型）、不变的成分协方差，但每组和每个成分的方差可变（平行因子分析模型）、零协方差且每组方差不同但每个成分方差相同（重复塔克3模型）以及严格不变性（对平均矩阵进行成分分析）。利用依恋理论的一个国际数据集，详细说明了这种不变模型的层次结构以及相互评估模型的程序。
