Principal components analysis: theory and application to gene expression data analysis

Todorov, Hristo; Fournier, David; Gerber, Susanne

doi:10.18547/gcb.2018.vol4.iss2.e100041

Cited by 40 publications

(36 citation statements)

References 8 publications

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“…determining how many components/factors should be extracted from a data reduction analysis, because this can greatly impact the interpretation, comparability, and replicability of structures derived from those analyses (e.g. Zwick, & Velicer, 1986, Todorov, Fournier, & Gerber, 2018. Most notably, statisticians largely agree that one extraction method, Kaiser's criterion, should never be used because it increases the risk of over-extraction compared to more automated tests, which in turn can lead to instability in the structures derived from data reduction analyses, and thus affect the overall interpretation of one's results.…”

Section: Introductionmentioning

confidence: 99%

Data reduction analyses of animal behaviour: avoiding Kaiser's criterion and adopting more robust automated methods

Morton

2019

Animal Behaviour

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Data reduction analyses like principal components and exploratory factor analyses identify relationships within a set of potentially correlated variables, and cluster correlated variables into a smaller overall quantity of groupings. Because of their relative objectivity, these analyses are popular throughout the animal literature to study a wide variety of topics. Numerous authors have highlighted "best practice" guidelines for component/factor "extraction", i.e. determining how many components/factors to extract from a data reduction analysis, because this can greatly impact the interpretation, comparability, and replicability of one's results. Statisticians agree that Kaiser's criterion, i.e. extracting components/factors with eigenvectors >1.0, should never be used yet within the animal literature, a considerable number of authors still use it, including publications as recent as 2018, and across a wide range of taxa (e.g. insects, birds, fish, mammals) and topics (e.g. personality, cognition, health, morphology, reproduction). It is therefore clear that further awareness is needed to target the animal sciences to ensure that results optimise structural stability, and thus, comparability and reproducibility. In the present commentary, we first clarify the distinction between principal components and exploratory factor analyses in terms of analysing simple versus complex structures, and how this relates to component/factor extraction. Second, we highlight empirical evidence from simulation studies to explain why certain extraction methods are more reliable than others, including why automated methods are better, and why Kaiser's criterion is inappropriate and should therefore never be used. Third, we provide recommendations on what to do if multiple automated extraction methods "disagree" which can arise when dealing with complex structures. Finally, we explain how to perform and interpret more robust and automated extraction tests using R.

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Section: Introductionmentioning

confidence: 99%

Data reduction analyses of animal behaviour: avoiding Kaiser's criterion and adopting more robust automated methods

Morton

2019

Animal Behaviour

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“…The first multivariate strategy we investigated was performing ANOVA tests on principal component (PC) scores obtained from the original variables. We used eigen decomposition of the population correlation matrix in order to calculate the PCs, which is the preferred approach when variables are measured on different scales [30,32]. Based on the Kaiser criterion, we only retained components whose corresponding eigenvalue was greater than one [33].…”

Section: Methods To Detect Treatment Effectsmentioning

confidence: 99%

“…Based on the Kaiser criterion, we only retained components whose corresponding eigenvalue was greater than one [33]. Component scores were obtained by multiplying the standardized data matrix of original variables with the eigenvectors of the population correlation matrix [32].…”

Section: Methods To Detect Treatment Effectsmentioning

confidence: 99%

“…In contrast, PCA is capable of overcoming the "large p, small n" problem by reducing the large number of variables to a few uncorrelated components. The method only imposes the constraint that the first component captures the direction of greatest variance in the data hyper-ellipsoid [32] and does not perform regression or classification of data. Therefore multicollinearity poses no issue.…”

Section: Plos Onementioning

confidence: 99%

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Applying univariate vs. multivariate statistics to investigate therapeutic efficacy in (pre)clinical trials: A Monte Carlo simulation study on the example of a controlled preclinical neurotrauma trial

2020

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Background Small sample sizes combined with multiple correlated endpoints pose a major challenge in the statistical analysis of preclinical neurotrauma studies. The standard approach of applying univariate tests on individual response variables has the advantage of simplicity of interpretation, but it fails to account for the covariance/correlation in the data. In contrast, multivariate statistical techniques might more adequately capture the multi-dimensional pathophysiological pattern of neurotrauma and therefore provide increased sensitivity to detect treatment effects. Results We systematically evaluated the performance of univariate ANOVA, Welch's ANOVA and linear mixed effects models versus the multivariate techniques, ANOVA on principal component scores and MANOVA tests by manipulating factors such as sample and effect size, normality and homogeneity of variance in computer simulations. Linear mixed effects models demonstrated the highest power when variance between groups was equal or variance ratio was 1:2. In contrast, Welch's ANOVA outperformed the remaining methods with extreme variance heterogeneity. However, power only reached acceptable levels of 80% in the case of large simulated effect sizes and at least 20 measurements per group or moderate effects with at least 40 replicates per group. In addition, we evaluated the capacity of the ordination techniques, principal component analysis (PCA), redundancy analysis (RDA), linear discriminant analysis (LDA), and partial least squares discriminant analysis (PLS-DA) to capture patterns of treatment effects without formal hypothesis testing. While LDA suffered from a high false positive rate due to multicollinearity, PCA, RDA, and PLS-DA were robust and PLS-DA outperformed PCA and RDA in capturing a true treatment effect pattern.

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“…Principal component analysis (PCA) is a statistical tool that is used to reduce data sets that are large and complex, whereby this reduction is made by transforming the data into new variables (principal components). These new variables house most of the dataset, becoming a few components, which facilitate the analysis and interpretation of the original data (Todorov, H., Fournier, D., Gerber, S., 2018)…”

Section: Methodsmentioning

confidence: 99%

Lessons From a Costs Analysis in Potato Production

et al. 2019

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The potato is one of the most widely cultivated horticultural crops in the world. Brazil ranks 21st among the world's largest potato producers, and the United States (US) is the fifth largest producer in the world. This study analyzes and compares the economic, financial aspects of potato production in the Vargem Grande do Sul region, SP (Brazil), and southwestern Idaho (US), seeking to identify which aspects of American production can serve as reference for technical and financial improvement of the Brazilian production. Data from official sources were analyzed using principal components analysis (PCA). Potato producer in Vargem Grande do Sul need learning how to reduce the factors of production costs to have better financial results in your potato production.

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Principal components analysis: theory and application to gene expression data analysis

Cited by 40 publications

References 8 publications

Data reduction analyses of animal behaviour: avoiding Kaiser's criterion and adopting more robust automated methods

Data reduction analyses of animal behaviour: avoiding Kaiser's criterion and adopting more robust automated methods

Applying univariate vs. multivariate statistics to investigate therapeutic efficacy in (pre)clinical trials: A Monte Carlo simulation study on the example of a controlled preclinical neurotrauma trial

Lessons From a Costs Analysis in Potato Production

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