Common Principle Components

Covariance matrices are a natural multivariate structure as input for various methods such as Structural Equations Modeling(SEM), Factor Analysis, Principle Components and Cluster Analysis to name a few. Almost all can be shown to be special cases of SEMs. Recently I came across the need to consider the question of Common Principle Components(CPC). The situation is a k-group setting involving questions about shared principle components among the k-groups. Note, this notion is not restricted to equality of covariance matrices. However this particular notion(CPC) is not directly estimated and tested within common statistical software such as SAS‘s Proc Calis or well known Lisrel. It turns out that this was the focus of statistican Bernhard Flury’s (1988) research. CPC software and references to Flury’s work can be found here.