Analysis of Correlation Matrices Using Scale-Invariant Common Principal Component Models and a Hierarchy of Relationships Between Correlation Matrices

作者：Gu Fei^*

来源：Structural Equation Modeling, 2016, 23(6): 819-826.

DOI：10.1080/10705511.2016.1207180

• common principal component model
• principal component analysis
• scale-invariant model

In this article, we demonstrate that the scale-invariant common principal component (CPC) model previously developed in the literature is in fact not scale invariant and cannot be used to analyze correlation matrices. To fill this gap, the correct formulation of the scale-invariant CPC model is provided, and an offspring scale-invariant CPC model is defined. Based on a series of scale-invariant CPC models, a hierarchy of relationships between correlation matrices is established. We illustrate the proposed scale-invariant CPC models with two numeric examples, and spend efforts on the interpretation of the common PCs in the second example. Some suggestions are given at the end regarding the software implementation of the scale-invariant CPC models.

• 出版日期2016-12
• 单位McGill