Comparison of correction factors and sample size required to test the equality of the smallest eigenvalues in principal component analysis

Eduard Gañan-Cardenas, Juan Carlos Correa-Morales

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

In the inferential process of Principal Component Analysis (PCA), one of the main challenges for researchers is establishing the correct number of components to represent the sample. For that purpose, heuristic and statistical strategies have been proposed. One statistical approach consists in testing the hypothesis of the equality of the smallest eigenvalues in the covariance or correlation matrix using a Likelihood-Ratio Test (LRT) that follows a χ2 limit distribution. Different correction factors have been proposed to improve the approximation of the sampling distribution of the statistic. We use simulation to study the significance level and power of the test under the use of these different factors and analyze the sample size required for an adequate approximation. The results indicate that for covariance matrix, the factor proposed by Bartlett offers the best balance between the objectives of low probability of Type I Error and high Power. If the correlation matrix is used, the factors WB and cχ2d are the most recommended. Empirically, we can observe that most factors require sample sizes 10 or 20 times the number of variables if covariance or correlation matrices, respectively, are implemented.

Translated title of the contributionComparación de los factores de correción y tamaños de muestra requeridos para probar la igualdad de los valores propios más pequeños en el análisis de componentes principales
Original languageEnglish
Pages (from-to)43-64
Number of pages22
JournalRevista Colombiana de Estadistica
Volume44
Issue number1
DOIs
Publication statusPublished - Jan 2021
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2021, Universidad Nacional de Colombia. All rights reserved.

All Science Journal Classification (ASJC) codes

  • Statistics and Probability

Fingerprint

Dive into the research topics of 'Comparison of correction factors and sample size required to test the equality of the smallest eigenvalues in principal component analysis'. Together they form a unique fingerprint.

Cite this