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Be careful with your principal components
Uppsala University, Disciplinary Domain of Science and Technology, Biology, Department of Ecology and Genetics, Animal ecology.ORCID iD: 0000-0001-5436-6989
2019 (English)In: Evolution, ISSN 0014-3820, E-ISSN 1558-5646, Vol. 73, no 10, p. 2151-2158Article in journal, Editorial material (Other academic) Published
Abstract [en]

Principal components analysis (PCA) is a common method to summarize a larger set of correlated variables into a smaller and more easily interpretable axes of variation. However, the different components need to be distinct from each other to be interpretable otherwise they only represent random directions. This is a fundamental assumption of PCA and, thus, needs to be tested every time. Sample correlation matrices will always result in a pattern of decreasing eigenvalues even if there is no structure. Tests are, therefore, needed to discern real patterns from illusionary ones. Furthermore, the loadings of the vectors need to be larger than expected by random data to be useful in the calculation of PC-scores. PC-scores calculated from nondistinct PC's have very large standard errors and cannot be used for biological interpretations. I give a number of examples to illustrate the potential problems with PCA. Robustness of the PC's increases with increasing sample size but not with the number of traits. I review a few simple test statistics appropriate for testing PC's and use a real-world example to illustrate how this can be done using randomization tests. PCA can be very useful but great care is needed to avoid spurious results.

Place, publisher, year, edition, pages
2019. Vol. 73, no 10, p. 2151-2158
Keywords [en]
Correlations, principal components analysis, randomization, standard error
National Category
Evolutionary Biology
Identifiers
URN: urn:nbn:se:uu:diva-398530DOI: 10.1111/evo.13835ISI: 000484684900001PubMedID: 31433858OAI: oai:DiVA.org:uu-398530DiVA, id: diva2:1375974
Available from: 2019-12-06 Created: 2019-12-06 Last updated: 2019-12-06Bibliographically approved

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Björklund, Mats

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