Confidence Areas for Fixed-Effects PCA

Principal component analysis (PCA) is often used to visualize data when the rows and the columns are both of interest. In such a setting, there is a lack of inferential methods on the PCA output. We study the asymptotic variance of a fixed-effects model for PCA, and propose several approaches to ass...

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Bibliographic Details
Published inJournal of computational and graphical statistics Vol. 25; no. 1; pp. 28 - 48
Main Authors Josse, Julie, Wager, Stefan, Husson, François
Format Journal Article
LanguageEnglish
Published Alexandria Taylor & Francis 02.01.2016
American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America
Taylor & Francis Ltd
Subjects
Confidence ellipses
Fixed-effects model
Jackknife
Machine Learning
Mathematical models
Methodology
Parametric bootstrap
Principal components analysis
Statistical inference
Statistics
Studies
Variability
Variables
Visualization
jackknife
parametric bootstrap
confidence ellipses
variability
fixed-effects model
PCA
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Summary:Principal component analysis (PCA) is often used to visualize data when the rows and the columns are both of interest. In such a setting, there is a lack of inferential methods on the PCA output. We study the asymptotic variance of a fixed-effects model for PCA, and propose several approaches to assessing the variability of PCA estimates: a method based on a parametric bootstrap, a new cell-wise jackknife, as well as a computationally cheaper approximation to the jackknife. We visualize the confidence regions by Procrustes rotation. Using a simulation study, we compare the proposed methods and highlight the strengths and drawbacks of each method as we vary the number of rows, the number of columns, and the strength of the relationships between variables.
ISSN:1061-8600
1537-2715
DOI:10.1080/10618600.2014.950871