Principal components analysis and canonical correlations analysis for three-mode data and their applications to questionnaire data

传统的因子分析法构建心理个体差异量表的过程存在两个明显的缺陷：（1）以项目间的内在一致性为基础，忽视了与外部信息的关系;结果表明，虽然各分量表具有较高的信度，但有时缺乏结构效度。（二）虽然具有复杂措辞的项目可以通过反映预期结构的一些微妙方面来提高效度，但由于与具有简单措辞的问题的相关性相对较低，因此具有复杂措辞的项目倾向于从分量表的定义中删除为“剩余项目”。这两个命题表明，应该探索不同的优化标准，这些标准可以为项目响应的线性组合产生或多或少不同的权重，主成分分析（PCA）。本文提出了两种新的心理测量技术，并对它们进行了比较。 ...更多信息 展示了它们克服上述缺点的可能性。第一个，修改tucker 2（三模式主成分分析的简化版本），表明它产生显着不同的权重集，从普通的PCA时，内部一致的项目的子集具有较高的相关性与外部变量比其他。此外，它也表明，人们可以平衡的“带宽保真度的困境”所造成的相关性的差异，通过改变二阶组件的数量。第二（组）的方法，正交和斜直接procrustes技术，表明可以获得（子）规模的模式近似理论上指定的目标矩阵在任何条件下，而解释的方差的量将是非常小的，如果目标是不全等的相关结构的给定数据。倾斜法优化模式（标准回归权重矩阵）而不是结构（相关矩阵）比正交法更好。少

The traditional procedure of scale construction for measuring psychological individual differences by the use of factor analytical method has two distinctive drawbacks:(1)It is based on internal consistency between items and ignores the relationships with external information. As the results, scores of (sub)scales sometimes lack of constructive validity although they have sufficiently high reliability.(2)Items with elaborated wordings tend to be removed from the definitions of subscales as 'remainder items' due to relatively low correlations with questions with simple wordings although they could contribute to increasing validity by reflecting some subtle aspects of intended constructs.These two propositions suggest that one should explore different optimization criteria which generate more or less different weights for linear composites of item responses from ones obtained from standard principal components analysis (PCA). We proposed two newly developed psychometric techniques, and d … More emonstrated their possibility to overcome drawbacks mentioned above. The first one, modified tucker2 (a simplified version of three-mode principal components analysis), showed that it generates remarkably different sets of weights from ordinary PCA when a subset of internally consistent items have higher correlations with external variables than others. In addition, it was also shown that one can balance the 'bandwidth-fidelity dilemma' caused by the differences of correlations by changing the number of the second-order components. The second (set of) methods, orthogonal and oblique direct procrustes techniques, demonstrated that one may obtain (sub)scales whose pattern approximate the theoretically specified target matrix in any conditions while the amount of explained variances would be very small if the target is not congruent to the correlational structure of the given data. Oblique method optimizing the pattern (the matrix of standard regression weights) rather than structure (the matrix of correlations) worked better than orthogonal one. Less