plt.perm {CCP}

Plot permutation distributions for test statistics

Description

This function plots permutation distributions for test statistics that are used to assign the statistical significance of canonical correlation coefficients, see function p.perm.

Usage

plt.perm(p.perm.out)

Arguments

p.perm.out

output of p.perm, see example below.

Details

Depending on what type of statistic was chosen in p.perm, a permutation distribution of this statistic is shown. The statistic is one of: Wilks' Lambda, Hotelling-Lawley Trace, Pillai-Bartlett Trace, or Roy's Largest Root. These test statistics can be used to assign significance levels to canonical correlation coefficients, for details see p.perm. The value corresponding to the "original" test statistic (calculated using the canonical correlation coefficients resulting from unpermuted data ) is plotted as a red, dotted vertical line; thus the area of the histogram outside this line determines the approximate p-value. The vertical line is not visible if the value corresponding to the original test statistic is in the far tail of the histogram, yielding a p-value which is (close to) zero. The numerical value corresponding to the original test statistic is plotted in the subtitle of the graph, as well as the calculated p-value. The grey vertical line represents the mean of the permutation distribution.

Author(s)

Uwe Menzel <[e-mail]>

See Also

See the function p.perm for the calculation of the p-values.

Examples

## Load the CCP package:
library(CCP)



## Simulate example data:
X <- matrix(rnorm(150), 50, 3)
Y <- matrix(rnorm(250), 50, 5)



## Calculate canonical correlations:
rho <- cancor(X,Y)$cor

## Define number of observations, 
## and number of dependent and independent variables:
N = dim(X)[1]       
p = dim(X)[2]   
q = dim(Y)[2]


## Plot the permutation distribution of an F approximation 
## for Wilks Lambda, considering 3 and 2 canonical correlations:
out1 <- p.perm(X, Y, nboot = 999, rhostart = 1)  
plt.perm(out1)    
out2 <- p.perm(X, Y, nboot = 999, rhostart = 2)  
plt.perm(out2) 


## Plot the permutation distribution of an F approximation 
## for the Pillai-Bartlett Trace, 
## considering 3, 2, and 1 canonical correlation(s):
res1 <- p.perm(X, Y, nboot = 999, rhostart = 1, type = "Pillai")  
plt.perm(res1)    
res2 <- p.perm(X, Y, nboot = 999, rhostart = 2, type = "Pillai")  
plt.perm(res2) 
res3 <- p.perm(X, Y, nboot = 999, rhostart = 3, type = "Pillai")  
plt.perm(res3)