Calculates a Principal Components Analysis with bootstrap confidence intervals for its parameters
PCA.Bootstrap(X, dimens = 2, Scaling = "Standardize columns", B = 1000, type = "np")
The type of Bootstrap used
Transformation of the raw data
Initial data provided to the function'
Transformed Data
Singular value decomposition of the transformed data
Row Scores for the initial Data
Correlation among variables and Principal Components for the Initial Data
Matrix containing the members of the Bootstrap Samples
Matrix containing the eigenvalues (columns) for each bootstrap sample (columns)
Matrix containing the proportions of accounted variance (columns) for each bootstrap sample (columns)
Three-dimensional array containing the left singular vectors for each bootstrap sample
Three-dimensional array containing the right singular vectors for each bootstrap sample
Projection of the bootstrap sampled matrix onto the bottstrap principal components
Projection of the bootstrap sampled matrix onto the bottstrap principal coordinates
Projection of the original matrix onto the bootstrap principal components
Correlation of the Initial Variabblñes and the PCs for each bootstrap sample
The original raw data matrix
Desired dimension of the solution.
Transformation that should be applied to the raw data.
Number of Bootstrap samples to draw.
Type of Bootstrap ("np", "pa", "spper", "spres")
Jose Luis Vicente Villardon
The types of bootstrap used are:
Non Parametric
parametric (data is obtained from a Multivariate Normal Distribution)
Semi-parametric Residuals are permutated
Semi-parametric Residuals are resampled
For the moment, only the non-parametric bootstrap is implemented.
The Principal Components (eigenvectors) are obtained using bootstrap samples.
The Row scotes are obtained projecting the completen data matrix into the bootstrap Principal Components. In this way all the individulas have the same number of replications.
Daudin, J. J., Duby, C., & Trecourt, P. (1988). Stability of principal component analysis studied by the bootstrap method. Statistics: A journal of theoretical and applied statistics, 19(2), 241-258.
Chateau, F., & Lebart, L. (1996). Assessing sample variability in the visualization techniques related to principal component analysis: bootstrap and alternative simulation methods. COMPSTAT, Physica-Verlag, 205-210.
Babamoradi, H., van den Berg, F., & Rinnan, Å. (2013). Bootstrap based confidence limits in principal component analysis—A case study. Chemometrics and Intelligent Laboratory Systems, 120, 97-105.
Fisher, A., Caffo, B., Schwartz, B., & Zipunnikov, V. (2016). Fast, exact bootstrap principal component analysis for p> 1 million. Journal of the American Statistical Association, 111(514), 846-860.
PCA.Biplot
if (FALSE) X=wine[,4:21]
grupo=wine$Group
rownames(X)=paste(1:45, grupo, sep="-")
pcaboot=PCA.Bootstrap(X, dimens=2, Scaling = "Standardize columns", B=1000)
plot(pcaboot, ColorInd=as.numeric(grupo))
summary(pcaboot)
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