Kroonenberg Pieter M, Oort Frans J
Department of Education, Leiden University, Leiden, The Netherlands.
Br J Math Stat Psychol. 2003 Nov;56(Pt 2):305-35. doi: 10.1348/000711003770480066.
Multimode covariance matrices, such as multitrait-multimethod matrices, contain the covariances of subject scores on variables for different occasions or conditions. This paper presents a comparison of three-mode component analysis and three-mode factor analysis applied to such covariance matrices. The differences and similarities between the non-stochastic and stochastic approaches are demonstrated by two examples, one of which has a longitudinal design. The empirical comparison is facilitated by deriving, as a heuristic device, a statistic based on the maximum likelihood function for three-mode factor analysis and its associated degrees of freedom for the three-mode component models. Furthermore, within the present context a case is made for interpreting the core array as second-order components.
多模式协方差矩阵，如多特质-多方法矩阵，包含了不同场合或条件下变量上主体分数的协方差。本文对应用于此类协方差矩阵的三模式成分分析和三模式因子分析进行了比较。通过两个例子展示了非随机方法和随机方法之间的差异与相似之处，其中一个例子具有纵向设计。通过推导一个基于三模式因子分析的最大似然函数及其三模式成分模型的相关自由度的统计量作为启发式工具，促进了实证比较。此外，在当前背景下，提出了将核心阵列解释为二阶成分的观点。
