Interpolating 95Th Percentile Eigenvalues from Random Data: An Empirical Example

Abstract

Selecting the "correct" number of components to retain in principal components analysis is crucial. Parallel analysis, which requires a comparison of eigenvalues from observed and random data, is a highly promising strategy for making this decision. This paper focuses on linear interpolation, which has been shown to be an accurate method of implementing parallel analysis. Specifically, this article contains tables of 95th percentile eigenvalues from random data that can be used when the sample size is between 50 and 500 and when the number of variables is between 5 and 50. An empirical example is provided illustrating linear interpolation, direct computation, and regression methods for obtaining 95th percentile eigenvalues from random data. The tables of eigenvalues given in this report will hopefully enable more researchers to use parallel analysis because interpolation is an accurate and simple method of obviating the Monte Carlo requirements of parallel analysis.