PARAN: Stata module to compute Horn's test of principal components/factors
paran is an implementation of Horn's technique for evaluating the components or factors retained in a principal components analysis (PCA) or a common factor analysis. According to Horn, a common interpretation of non-correlated data is that they are perfectly non-collinear, and one would expect therefore to see eigenvalues equal to 1 in a PCA of such data. However, Horn notes that multi-colinearity occurs due to sampling error and least-squares "bias," even in uncorrelated data, and therefore actual PCAs of such data will reveal eigenvalues of components greater than and less than 1. His strategy is to contrast eigenvalues produced through a PCA on a random dataset (uncorrelated variables) with the same number of variables and observations as the experimental or observational dataset to produce eigenvalues for components or factors that are adjusted for the sample error-induced inflation.
principal components, collinearity, factor analysis, parallel analysis
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