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Be careful with your principal components
Author(s) -
Björklund Mats
Publication year - 2019
Publication title -
evolution
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.84
H-Index - 199
eISSN - 1558-5646
pISSN - 0014-3820
DOI - 10.1111/evo.13835
Subject(s) - spurious relationship , principal component analysis , statistics , eigenvalues and eigenvectors , robustness (evolution) , sample size determination , set (abstract data type) , pattern recognition (psychology) , sample (material) , mathematics , biology , computer science , artificial intelligence , biochemistry , physics , chemistry , chromatography , quantum mechanics , gene , programming language
Abstract 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.