Function to perform a test of dimensionality

This functions allow to test for the number of axes in multivariate analysis. The procedure testdim.pca implements a method for principal component analysis on correlation matrix. The procedure is based on the computation of the RV coefficient.

Usage

testdim(object, ...)
# S3 method for pca
testdim(object, nrepet = 99, nbax = object$rank, alpha = 0.05, ...)

Arguments

object: an object corresponding to an analysis (e.g. duality diagram, an object of class dudi)
nrepet: the number of repetitions for the permutation procedure
nbax: the number of axes to be tested, by default all axes
alpha: the significance level
...: other arguments

Value

An object of the class krandtest. It contains also:

nb: The estimated number of axes to keep
nb.cor: The number of axes to keep estimated using a sequential Bonferroni procedure

References

Dray, S. (2008) On the number of principal components: A test of dimensionality based on measurements of similarity between matrices. Computational Statistics and Data Analysis, Volume 52, 2228--2237. doi:10.1016/j.csda.2007.07.015

Author

Stéphane Dray stephane.dray@univ-lyon1.fr

Examples

tab <- data.frame(matrix(rnorm(200),20,10))
pca1 <- dudi.pca(tab,scannf=FALSE)
test1 <- testdim(pca1)
test1
#> class: krandtest lightkrandtest 
#> Monte-Carlo tests
#> Call: testdim.pca(object = pca1)
#> 
#> Number of tests:   10 
#> 
#> Adjustment method for multiple comparisons:   none 
#> Permutation number:   99 
#>       Test       Obs    Std.Obs   Alter Pvalue
#> 1   Axis 1 0.5923081 -0.1620144 greater   0.54
#> 2   Axis 2 0.5285317 -1.8071384 greater   0.99
#> 3   Axis 3 0.5903391 -0.9589534 greater   0.84
#> 4   Axis 4 0.5851335 -1.0277549 greater   0.85
#> 5   Axis 5 0.6572883  0.1123162 greater   0.45
#> 6   Axis 6 0.6547971  0.3919727 greater   0.26
#> 7   Axis 7 0.7134174  1.1958308 greater   0.14
#> 8   Axis 8 0.8443807  4.1360788 greater   0.01
#> 9   Axis 9 0.8967238  4.2287495 greater   0.01
#> 10 Axis 10 1.0000000  6.5991361 greater   0.01
#> 
test1$nb
#> [1] 0
test1$nb.cor
#> [1] 0
data(doubs)
pca2 <- dudi.pca(doubs$env,scannf=FALSE)
test2 <- testdim(pca2)
test2
#> class: krandtest lightkrandtest 
#> Monte-Carlo tests
#> Call: testdim.pca(object = pca2)
#> 
#> Number of tests:   11 
#> 
#> Adjustment method for multiple comparisons:   none 
#> Permutation number:   99 
#>       Test       Obs    Std.Obs   Alter Pvalue
#> 1   Axis 1 0.9276029  9.8230582 greater   0.01
#> 2   Axis 2 0.8765561  6.1643389 greater   0.01
#> 3   Axis 3 0.8195407 -1.1692191 greater   0.89
#> 4   Axis 4 0.7130800  0.8246494 greater   0.21
#> 5   Axis 5 0.7621707  2.0138184 greater   0.04
#> 6   Axis 6 0.7781209  2.4575465 greater   0.04
#> 7   Axis 7 0.8316557  4.8180087 greater   0.01
#> 8   Axis 8 0.9641126  5.1280553 greater   0.01
#> 9   Axis 9 0.7978495  1.3216083 greater   0.13
#> 10 Axis 10 0.9701563  6.8085521 greater   0.01
#> 11 Axis 11 1.0000000  8.7154388 greater   0.01
#> 
test2$nb
#> [1] 2
test2$nb.cor
#> [1] 2