Br J Math Stat Psychol. 2007 Nov;60:295-314. doi: 10.1348/000711006X109636.

Estimating confidence intervals for principal component loadings: a comparison between the bootstrap and asymptotic results.

The British journal of mathematical and statistical psychology

Marieke E Timmerman, Henk A L Kiers, Age K Smilde

PMID: 17971271 DOI: 10.1348/000711006X109636

Abstract

Confidence intervals (CIs) in principal component analysis (PCA) can be based on asymptotic standard errors and on the bootstrap methodology. The present paper offers an overview of possible strategies for bootstrapping in PCA. A motivating example shows that CI estimates for the component loadings using different methods may diverge. We explain that this results from both differences in quality and in perspective on the rotational freedom of the population loadings. A comparative simulation study examines the quality of various estimated component loading CIs. The bootstrap approach is more flexible and generally yields better CIs than the asymptotic approach. However, in the case of a clear simple structure of varimax rotated loadings, one can be confident that the asymptotic estimates are reasonable as well.

MeSH terms

• Confidence Intervals*
• Humans
• Models, Psychological*
• Psychology / methods
• Psychology / statistics & numerical data

Publication Types

• Journal Article