Influence Diagnostics in Common Principal Components Analysis

In principal components analysis, the influence function and local influence approaches have been well established as important diagnostic tools. In this article, we first review the generalized local influence approach in the restricted likelihood framework. We then apply the restricted likelihood local influence diagnostic in the common principal components analysis. One special part of this local influence result is an elliptical norm of the empirical influence function, which is comparable to the deletion diagnostic scaled by the same matrix which requires iterative solutions for parameter estimates with every case deleted. Local influence diagnostics are constructed by some basic building blocks that are obtained directly from the maximum likelihood estimates of the parameters, and which are based on the original data and thus require less computation. A numerical example illustrates the technique and some joint influence effects are identified by the proposed method.