Bootstrap based confidence limits in principal component analysis — A case study

Babamoradi, Hamid; Berg, Franciscus Winfried J van der; Rinnan, Åsmund

doi:10.1016/j.chemolab.2012.10.007

Cited by 77 publications

(65 citation statements)

References 38 publications

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“…Each sub-model, both with respect to Jack-knifing and bootstrap sample, was rotated and mirrored towards the model on the calibrated data. This is a common method to ascertain that the estimates are not over estimated (Babamoradi et al, 2013). The uncertainty estimates for loading weights were subsequently estimated based on different amounts of split-half runs, and compared to the uncertainty estimate for leave-one-respondent out.…”

Section: Discussionmentioning

confidence: 99%

“…This is a particularly relevant problem for CATA data since this method is commonly applied with a large number of respondents (e.g., 60-80 or more), and thus the difference between each sub-model is very small. A better and more sophisticated method for estimating the uncertainty in the model parameters is bootstrapping (Babamoradi, van den Berg, & Rinnan, 2013;Wehrens, Putter, Lutgarde, & Buydens, 2000). A drawback for this method is that it is not so straightforward to apply.…”

Section: Pls and Jack-knifing Theorymentioning

confidence: 99%

See 1 more Smart Citation

Check-all-that-apply data analysed by Partial Least Squares regression

Rinnan

Giacalone

Frøst

2015

Food Quality and Preference

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Section: Discussionmentioning

confidence: 99%

Section: Pls and Jack-knifing Theorymentioning

confidence: 99%

Check-all-that-apply data analysed by Partial Least Squares regression

Rinnan

Giacalone

Frøst

2015

Food Quality and Preference

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“…37 The number of bootstrap samples was 1,000 × the number of fitted parameter triplets, i.e., in total 101,000 for the 101 subjects.…”

Section: Quantificationmentioning

confidence: 99%

Quantification of Blood Flow-Dependent Component in Estimates of Beta-Amyloid Load Obtained Using Quasi-Steady-State Standardized Uptake Value Ratio

Cselényi

Farde

2015

J Cereb Blood Flow Metab

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Longitudinal positron emission tomography (PET) imaging of beta-amyloid is used in basic research and in drug efficacy trials in Alzheimer's disease (AD). However, the extent of amyloid accumulation after clinical onset is not fully known. Importantly, regional PET data are typically quantified using the standardized uptake value ratio (SUVR), which according to simulations is sensitive to changes in regional cerebral blood flow (rCBF). We aimed to better understand the potentials of longitudinal amyloid imaging by disentangling the influence of blood flow on SUVR using experimental data.[18F]AV-45 PET data from 101 subjects, ranging from cognitively normal to AD patients, in the Alzheimer's Disease Neuroimaging Initiative were extracted. The relationship between global cortical distribution volume ratio, indicator of rCBF (R1), and SUVR was examined using multilinear regression. There was a significant effect of rCBF on SUVR. The effect increased by disease severity. Results suggest that changes in rCBF can produce apparent changes in SUVR in AD. Therefore, future longitudinal studies should measure amyloid changes in a way not sensitive to this effect, ideally using quantitative PET imaging. Furthermore, the results suggest no true accumulation beyond clinical onset and highlight the risks of longitudinal amyloid imaging in drug trials in AD.

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“…It has also been suggested that the sign of each PC should be switched based on the correlation between the columns of V b and the columns of V , rather than the dot products

V_{false[, k false]}^{b'} V_{false[, k false]}

(Jackson, 1995; Babamoradi et al, 2012). 3 We advocate against this correlation method, in favor of the cross product method.…”

Section: Full Description Of the Bootstrap Pca Algorithmmentioning

confidence: 99%

“…Others have argued if the parameter of interest is the principal subspace or the model fit, then the bootstrap PCs should be adjusted to correct for rotational variability, as the principal subspace is unaffected by rotations among the leading PCs. Specifically, it has been suggested to use a Procrustean rotation to match the bootstrap PCs to the original sample PCs (Milan and Whittaker, 1995), and to then create pointwise confidence intervals (CIs) based on the rotated PCs (Timmerman et al, 2007; Babamoradi et al, 2012). 5 We argue however that bootstrap rotational variability is informative of genuine sampling rotational variability, and that adjusting for rotations is not an appropriate way to represent sampling variability of the principal subspace, or the sampling variability of model fit.…”

Section: Full Description Of the Bootstrap Pca Algorithmmentioning

confidence: 99%

Fast, Exact Bootstrap Principal Component Analysis for p > 1 Million

Fisher¹,

Caffo²,

Schwartz³

et al. 2016

Journal of the American Statistical Association

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Many have suggested a bootstrap procedure for estimating the sampling variability of principal component analysis (PCA) results. However, when the number of measurements per subject (p) is much larger than the number of subjects (n), calculating and storing the leading principal components from each bootstrap sample can be computationally infeasible. To address this, we outline methods for fast, exact calculation of bootstrap principal components, eigenvalues, and scores. Our methods leverage the fact that all bootstrap samples occupy the same n-dimensional subspace as the original sample. As a result, all bootstrap principal components are limited to the same n-dimensional subspace and can be efficiently represented by their low dimensional coordinates in that subspace. Several uncertainty metrics can be computed solely based on the bootstrap distribution of these low dimensional coordinates, without calculating or storing the p-dimensional bootstrap components. Fast bootstrap PCA is applied to a dataset of sleep electroencephalogram recordings (p = 900, n = 392), and to a dataset of brain magnetic resonance images (MRIs) (p ≈ 3 million, n = 352). For the MRI dataset, our method allows for standard errors for the first 3 principal components based on 1000 bootstrap samples to be calculated on a standard laptop in 47 minutes, as opposed to approximately 4 days with standard methods.

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Bootstrap based confidence limits in principal component analysis — A case study

Cited by 77 publications

References 38 publications

Check-all-that-apply data analysed by Partial Least Squares regression

Check-all-that-apply data analysed by Partial Least Squares regression

Quantification of Blood Flow-Dependent Component in Estimates of Beta-Amyloid Load Obtained Using Quasi-Steady-State Standardized Uptake Value Ratio

Fast, Exact Bootstrap Principal Component Analysis for p > 1 Million

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