BootCCA: Bootstrap for Canonical Correlation Analysis (CCA).

In HerveAbdi/data4PCCAR: Some data sets and R-functions for PCA and CA to accompany Abdi & Beaton (to appear, 2023) Principal Component and Correspondence Analysis with R

Bootstrap for Canonical Correlation Analysis (CCA).

Description

Boot4CCA: Creates "Bootstrap Bricks" and other bootstrap statistics for the I and J sets of a CCA. The bricks are obtained from bootstrapping the rows of the two data-tables used for the CCA. Boot4CCA uses the "transition formula" to get the values of the row and column loadings from multiplication of the latent variables. Gives also the bootstrapped eigenvalues (if eigen = TRUE).

Usage

Boot4CCA(
  DATA1,
  DATA2,
  center1 = TRUE,
  center2 = TRUE,
  scale1 = "SS1",
  scale2 = "SS1",
  Fi = NULL,
  Fj = NULL,
  nf2keep = 3,
  nIter = 1000,
  critical.value = 2,
  eig = FALSE,
  alphaLevel = 0.05
)

Arguments

DATA1	an N*I data matrix
DATA2	an N*J data matrix (measured on the same observations as DATA2)
center1	when TRUE (default) DATA1 will be centered
center2	when TRUE (default) DATA2 will be centered
scale1	when TRUE (default) DATA1 will be normalized. Depends upon function scale0 whose description is: boolean, text, or (numeric) vector. If boolean or vector, it works just as scale. The following text options are available: 'z': z-score normalization, 'sd': standard deviation normalization, 'rms': root mean square normalization, 'ss1': sum of squares (of columns) equals 1 (i.e., each column vector has length of 1).
scale2	when TRUE (default) DATA2 will be normalized (same options as for scale1).
Fi	(Default = NULL), the I factor scores for the columns of DATA1. if NULL, Boot4RowCA computes them..
Fj	= (Default = NULL, the J factor scores for the columns of DATA2. if NULL the function Boot4RowCA computes them.
nf2keep	How many factors to keep for the analysis (Default = 3).
nIter	(Default = 1000). Number of Iterations (i.e., number of Bootstrtap samples).
critical.value	(Default = 2). The critical value for a BR to be considered significant.
eig	if TRUE compute bootstraped confidence intervals (CIs) for the eigenvalues (default is FALSE).
alphaLevel	the alpha level used to compute the confidence intervals for the eigenvalues (with CIS at 1-alpha). Default is .05

Details

Note: Boot4CCA gives the eigenvalues of the matrix X'Y even though CCA works with the singular values (i.e., the square roots of the eigenvalues) of X'Y.

Value

a list with

• bootstrapBrick.i: the the I * Dimensions * Iterations Brick of Bootstraped factor scores for the I-set;

• bootRatios.i: the bootstrap ratios for the I-set;

• bootRatiosSignificant.i: the Significant BRs for the I-set;

• bootstrapBrick.j: the J * Dimensions * Iterations Brick of Bootstraped factor scores for the J-set;

• bootRatios.j: the bootstrap ratios for the J-set;

• bootRatiosSignificant.j: the Significant BRs for the J-set;

In addition if eig = TRUE, the list includes:

• eigenValues: the nIter * nL table of eigenvalues;

• fixedEigenvalues: the eigenvalues of matrix nX'Y.

• eigenCIs: the CIs for the eigenvalues.

Author(s)

Vincent Guillemot & Hervé Abdi

See Also

scale0

Examples

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HerveAbdi/data4PCCAR documentation built on Sept. 11, 2022, 4:19 p.m.