Seeing distinct groups where there are none: spurious patterns from between-group PCA

Cardini, A.; O’Higgins, Paul; Rohlf, F. James

doi:10.1101/706101

Cited by 13 publications

(21 citation statements)

References 60 publications

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“…Similarly, the score on bgPC1 from the simulation at upper center correlates 0.83 with the actual simulated factor score, and likewise correctly fails to separate the groups, whereas once again component bgPC2 is wholly fictional. Note the striking similarity of the panel at upper center in this figure to the lower right panel of Figure 1 of Cardini et al (2019), a three-group analysis based on a real GMM data set, although likewise with wholly fictional groups.…”

Section: Some Aspects Of Truth Persist In Spite Of the Pathologiesmentioning

confidence: 54%

“…Acknowledgements Andrea Cardini (University of Modena and University of Western Australia) was the first in our group to notice bgPCA's clustering pathology, and the idea of a pair of papers scrutinizing applications of bgPCA to high-dimensional GMM data sets, particularly insofar as they ignore the implications of the MPT, was his. Our discussion sharpened over many months of interaction also involving Jim Rohlf (Stony Brook University), and Paul O'Higgins (University of York), discussions leading to Cardini et al (2019) as well as this paper. Norm MacLeod (London and University of Nanjing) guided me through a thoughtful review of the twentieth-century origins of the method criticized here, and Michael Perlman (University of Washington) was a helpful guide into the literature of the MPT at the time all this work began.…”

Section: Concluding Observationsmentioning

confidence: 87%

“…2 for twice as many variables, 600 instead of 300, hence y = p∕n = 20. The configuration of group centroids remains equilateral even as the visual separation of the groups increases in proportion to the square-root of the eigenvalues (here reported as PLS totals of explained squared covariance) 21;in 2016, 14;in 2017, 21;in 2018, 24;in 2019, through September 21, 34. The present note is a companion piece to Cardini et al (2019), which arrives at the same diagnosis as mine of the first pathology, that of fictitious clustering, somewhat less formally, without invoking the MPT but with several more realistic simulations and simpler algebra. The two approaches, one more biomathematical and one less so, end up offering the same advice: the technique of bgPCA should never be used with GMM data that have sufficiently many shape coordinates to represent the form evocatively-in other words, data sets consisting mostly of closely spaced semilandmarks: exactly the GMM data sets that sustain today's most seductive visualizations.…”

Section: Introductionmentioning

confidence: 89%

“…The techniques of bgPCA and PLS are still identical, and likewise the fictitious "finding" of perfect separation, but the symmetry of the plots in Figs. 1 and 2 appears to be broken figures offer the greatest possible apparent clustering, which is to say, the maximum possible misinformation in this situation, or, in the language of Cardini et al (2019), the greatest possible bias in the visual impression of separation. For four groups under the null model, bgPCA yields the greatest possible sum of squares of the intercentroid edge-lengths in diagrams like Fig.…”

Section: Introductionmentioning

confidence: 92%

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Pathologies of Between-Groups Principal Components Analysis in Geometric Morphometrics

Bookstein

2019

Evol Biol

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Good empirical applications of geometric morphometrics (GMM) typically involve several times more variables than specimens, a situation the statistician refers to as "high p/n," where p is the count of variables and n the count of specimens. This note calls your attention to two predictable catastrophic failures of one particular multivariate statistical technique, between-groups principal components analysis (bgPCA), in this high-p/n setting. The more obvious pathology is this: when applied to the patternless (null) model of p identically distributed Gaussians over groups of the same size, both bgPCA and its algebraic equivalent, partial least squares (PLS) analysis against group, necessarily generate the appearance of huge equilateral group separations that are fictitious (absent from the statistical model). When specimen counts by group vary greatly or when any group includes fewer than about ten specimens, an even worse failure of the technique obtains: the smaller the group, the more likely a bgPCA is to fictitiously identify that group as the end-member of one of its derived axes. For these two reasons, when used in GMM and other high-p/n settings the bgPCA method very often leads to invalid or insecure biological inferences. This paper demonstrates and quantifies these and other pathological outcomes both for patternless models and for models with one or two valid factors, then offers suggestions for how GMM practitioners should protect themselves against the consequences for inference of these lamentably predictable misrepresentations. The bgPCA method should never be used unskeptically-it is always untrustworthy, never authoritative-and whenever it appears in partial support of any biological inference it must be accompanied by a wide range of diagnostic plots and other challenges, many of which are presented here for the first time.Keywords Between-group principal components analysis · Ratio of variables to cases · High-p/n data sets · Discriminant function analysis in high dimensions · Factor analysis and discrimination · The Marchenko-Pastur theorem · Geometric morphometrics · Predictable mistakes in biometric data analysis · Effects of varying group size · Alternatives to canonical variates analysis

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Section: Some Aspects Of Truth Persist In Spite Of the Pathologiesmentioning

confidence: 54%

Section: Concluding Observationsmentioning

confidence: 87%

Section: Introductionmentioning

confidence: 89%

Section: Introductionmentioning

confidence: 92%

See 2 more Smart Citations

Pathologies of Between-Groups Principal Components Analysis in Geometric Morphometrics

Bookstein

2019

Evol Biol

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“…We performed bgPCA because it extracts fewer principal components that explain most of the variation in the data; as a result, a low‐dimensional PCA plot is reliable for understanding high dimensional multivariate data. However, since bgPCA can suffer from limitations (Cardini, O’Higgins & Rohlf, 2019), we also tested independently for significant differences between species and groups based on morphological data using permutations multivariate analysis of variance (PERMANOVA) (Anderson, 2001). PERMANOVA tests the null hypothesis that the centroids and dispersion of the groups are equivalent for all groups.…”

Section: Methodsmentioning

confidence: 99%

Diversity, phylogeny and biogeography of Systomus (Teleostei, Cyprinidae) in Sri Lanka

et al. 2020

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The South and SouthEast Asian freshwater fish genus Systomus (Cyprinidae) comprises 17 valid species. Six nominal species, including three endemics, have been reported from Sri Lanka, a continental island separated from India by a shallow-shelf sea. The species diversity of Systomus on the island has until now not been assessed; neither has an evaluation been made of their phylogenetic history. Here, based on an analysis of the nuclear recombination activating protein 1 (rag1), and mitochondrial cytochrome c oxidase subunit 1 (cox1) and cytochrome b (cytb) gene markers, and a morphological examination of 143 specimens from 49 locations in Sri Lanka, we reassess the diversity of Systomus on the island and analyse patterns of their evolution and biogeography. Divergence-time estimates, based on a substitution rate calibration, date the basal split between Systomus and its sister group, the Afrotropical small barbs, to 30.0 Ma (95% highest posterior density: 25.4-35.2 Ma). The species of Systomus belong to two distinct clades. The first includes the Sri Lankan endemics S. asoka, S. martenstyni and S. pleurotaenia, which comprise an insular diversification following the immigration of a common ancestor during the Oligocene. The second, which includes the remaining species of Indian, Sri Lankan and SouthEast Asian Systomus, has a crown age dating to the Late Miocene. Morphological and molecular species delimitation analyses failed to validate the two nominal species, S. spilurus and S. timbiri, previously reported from Sri Lanka: both are considered synonyms of S. sarana, as are the nomina S. chryseus, S. chrysopoma, S. laticeps, S. rufus, S. pinnauratus and S. subnasutus. Four genetically and geographically discrete lineages of S. sarana occur in the island, and three in India. Molecular species delimitation analysis suggests these all belong to a single species, S. sarana. The genetically distinct Sri Lankan populations of S. sarana result from Plio-Pleistocene dispersal or vicariance events between India and Sri Lanka-as a result of emergence and inundation of the now submerged isthmus connecting the two landmasses-as well as autochthonous insular diversification.

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The evolution of palate shape in the Lepilemur‐Cheirogaleidae clade (Primates: Strepsirrhini)

Andrews

Masters

Génin

et al. 2020

American J Phys Anthropol

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Objectives Phylogenies consistently group the folivorous Lepilemur species with the small‐bodied insectivorous‐frugivorous cheirogaleids. Juvenile lepilemurs and adult cheirogaleids share allometries in most aspects of skull morphology, except the palate. We investigated potential influences on palate shape in these taxa and several outgroups using geometric morphometrics. Materials and Methods Our sample included representatives of four extant strepsirrhine families, Cheirogaleidae (including Lepilemurinae), Lemuridae, Indriidae, and Galagidae, and one subfossil Megaladapis. Our dataset comprised 32 landmarks collected from 397 specimens representing 15 genera and 28 species, and was analyzed using generalized procrustes analyses and between group principal component analysis. We explored the influence of size, phylogeny, diet, and the propagation of loud vocalizations on palate shape. Results While congeneric species clustered within the morphospace, the phylomorphospace did not mirror molecular phylogenetic hypotheses of higher‐order relationships. Four palate forms were distinguished within the Cheirogaleidae. Diet, strongly linked to body size, had the single greatest influence on palate shape. The production of long‐distance advertisement calls was most often associated with positive scores on the PC1 axis. Discussion Our results suggest that the extensive variation in palate shape among Cheirogaleidae is related to dietary shifts that accompanied changes in body size during the clade's radiation. Molecular phylogenies indicate that cheirogaleid diversification involved repeated dwarfing events, which in turn drove dietary shifts from ancestral folivory‐frugivory to frugivory, gummivory, and faunivory in the descendant species. The elongated Lepilemur palate is probably related to accelerated eruption of the cheek teeth to render juveniles competent to shear leaves upon weaning.

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Seeing distinct groups where there are none: spurious patterns from between-group PCA

Cited by 13 publications

References 60 publications

Pathologies of Between-Groups Principal Components Analysis in Geometric Morphometrics

Pathologies of Between-Groups Principal Components Analysis in Geometric Morphometrics

Diversity, phylogeny and biogeography of Systomus (Teleostei, Cyprinidae) in Sri Lanka

The evolution of palate shape in the Lepilemur‐Cheirogaleidae clade (Primates: Strepsirrhini)

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