eigenBootParallel function

Bootstrapping of the Eigenvalues From a Data Frame

The eigenBootParallel function samples observations from a data.frame to produce correlation or covariance matrices from which eigenvalues are computed. The function returns statistics about these bootstrapped eigenvalues. Their means or their quantile could be used later to replace the eigenvalues inputted to a parallel analysis. The eigenBootParallel can also compute random eigenvalues from empirical data by column permutation (Buja and Eyuboglu, 1992).

eigenBootParallel(x, quantile = 0.95, nboot = 30,
  option = "permutation", cor = TRUE, model = "components", ...)

Arguments

• x: data.frame: data from which a correlation matrix will be obtained
• quantile: numeric: eigenvalues quantile to be reported
• nboot: numeric: number of bootstrap samples
• option: character: "permutation" or "bootstrap"
• cor: logical: if TRUE computes eigenvalues from a correlation matrix, else from a covariance matrix (eigenComputes)
• model: character: bootstraps from a principal component analysis ("components") or from a factor analysis ("factors")
• ...: variable: additionnal parameters to give to the cor or cov functions

Returns

• values: data.frame: mean, median, quantile, standard deviation, minimum and maximum of bootstrapped eigenvalues

Examples

# .......................................................
# Example from the iris data
 eigenvalues <- eigenComputes(x=iris[,-5])

# Permutation parallel analysis distribution
 aparallel   <- eigenBootParallel(x=iris[,-5], quantile=0.95)$quantile

# Number of components to retain
 results     <- nScree(x = eigenvalues, aparallel = aparallel)
 results$Components
 plotnScree(results)
# ......................................................

# ......................................................
# Bootstrap distributions study of the eigenvalues from iris data
# with different correlation methods
 eigenBootParallel(x=iris[,-5],quantile=0.05,
                   option="bootstrap",method="pearson")
 eigenBootParallel(x=iris[,-5],quantile=0.05,
                   option="bootstrap",method="spearman")
 eigenBootParallel(x=iris[,-5],quantile=0.05,
                   option="bootstrap",method="kendall")

References

Buja, A. and Eyuboglu, N. (1992). Remarks on parallel analysis. Multivariate Behavioral Research, 27(4), 509-540.

Zwick, W. R. and Velicer, W. F. (1986). Comparison of five rules for determining the number of components to retain. Psychological bulletin, 99, 432-442.

See Also

principalComponents, iterativePrincipalAxis, rRecovery

Author(s)

Gilles Raiche

Centre sur les Applications des Modeles de Reponses aux Items (CAMRI)

Universite du Quebec a Montreal

raiche.gilles@uqam.ca