main_tracyWidom: Tracy-Widom test for eigenvalues

In LEA: LEA: an R package for Landscape and Ecological Association Studies

Description

Perform tracy-widom tests on a set of eigenvalues to determine the number of significative eigenvalues and calculate the percentage of variance explained by each principal component. For an example, see pca.

Usage

tracy.widom (object)

Arguments

object

a pcaProject object.

Value

tracy.widom returns a list containing the following components:

eigenvalues	The sorted input vector of eigenvalues (by descreasing order).
twstats	The vector of tracy-widom statistics.
pvalues	The vector of p-values associated with each eigenvalue.
effecn	The vector of effective sizes.
percentage	The vector containing the percentage of variance explained by each principal component.

Author(s)

Eric Frichot

References

Tracy CA and Widom H. (1994). Level spacing distributions and the bessel kernel. Commun Math Phys. 161 :289–309. Patterson N, Price AL and Reich D. (2006). Population structure and eigenanalysis. PLoS Genet. 2 :20.

See Also

pca lfmm.data lfmm

Examples

# Creation of the genotype file "genotypes.lfmm"
# with 1000 SNPs for 165 individuals.
data("tutorial")
write.lfmm(tutorial.R,"genotypes.lfmm")

#################
# Perform a PCA #
#################

# run of PCA
# Available     options, K (the number of PCs calculated), 
#               center and scale. 
# Creation of   genotypes.pcaProject - the pcaProject object.
#               a directory genotypes.pca containing:
# Create files: genotypes.eigenvalues - eigenvalues,    
#               genotypes.eigenvectors - eigenvectors,
#               genotypes.sdev - standard deviations,
#               genotypes.projections - projections,
# Create a pcaProject object: pc.
pc = pca("genotypes.lfmm", scale = TRUE)

#############################
# Perform Tracy-Widom tests #
#############################

# Perfom Tracy-Widom tests on all eigenvalues.
# Create file:  genotypes.tracyWidom - tracy-widom test information, 
#               in the directory genotypes.pca/.
tw = tracy.widom(pc)

# Plot the percentage of variance explained by each component.
plot(tw$percentage)

# Display the p-values for the Tracy-Widom tests. 
tw$pvalues

# remove pca Project
remove.pcaProject("genotypes.pcaProject")

Example output

[1] "genotypes.lfmm"
[1] "******************************"
[1] " Principal Component Analysis "
[1] "******************************"
summary of the options:

        -n (number of individuals)          50
        -L (number of loci)                 400
        -K (number of principal components) 50
        -x (genotype file)                  /work/tmp/genotypes.lfmm
        -a (eigenvalue file)                /work/tmp/genotypes.pca/genotypes.eigenvalues
        -e (eigenvector file)               /work/tmp/genotypes.pca/genotypes.eigenvectors
        -d (standard deviation file)        /work/tmp/genotypes.pca/genotypes.sdev
        -p (projection file)                /work/tmp/genotypes.pca/genotypes.projections
        -s data centered and scaled 

[1] "*******************"
[1] " Tracy-Widom tests "
[1] "*******************"
summary of the options:

        -n (number of eigenvalues)          50
        -i (input file)                     /work/tmp/genotypes.pca/genotypes.eigenvalues
        -o (output file)                    /work/tmp/genotypes.pca/genotypes.tracywidom
 [1] 8.000e-09 8.000e-09 8.000e-09 1.503e-04 3.152e-02 4.215e-01 6.565e-01
 [8] 6.859e-01 6.738e-01 9.363e-01 7.937e-01 9.827e-01 9.709e-01 9.425e-01
[15] 9.240e-01 8.119e-01 9.734e-01 9.870e-01 9.996e-01 9.972e-01 9.973e-01
[22] 9.904e-01 9.959e-01 9.835e-01 9.953e-01 9.777e-01 9.801e-01 9.354e-01
[29] 8.465e-01 9.499e-01 8.092e-01 8.500e-01 7.492e-01 9.638e-01 9.114e-01
[36] 8.908e-01 9.402e-01 9.173e-01 7.407e-01 8.460e-01 8.067e-01 7.215e-01
[43] 4.396e-01 2.428e-01 6.246e-01 2.789e-01 6.168e-01 3.909e-01 7.257e-01
[1] TRUE

LEA documentation built on Nov. 8, 2020, 8:19 p.m.