Comparison of Correction Factors and Sample Size Required to Test the Equality of the Smallest Eigenvalues in Principal Component Analysis

In the inferential process of Principal Component Analysis (PCA), one main challenges for researchers is establishing correct number components to represent sample. For that purpose, heuristic and statistical strategies have been proposed. One approach consists in testing hypothesis equality smallest eigenvalues covariance or correlation matrix using a Likelihood-Ratio Test (LRT) follows χ2 limit distribution. Different correction factors proposed improve approximation sampling distribution statistic. We use simulation study significance level power test under these different analyze sample size required an dequate approximation. The results indicate matrix, factor by Bartlett offers best balance between objectives low probability Type I Error high Power. If used, W ∗ cχ2 are most recommended. Empirically, we can observe require sizes 10 20 times variables if correlationmatrices, respectively, implemented.