NonParametric Jackstraw for Principal Component Analysis (PCA)
Description
Estimates statistical significance of association between variables and their principal components (PCs).
Usage
1 2 3 4 5 6 
Arguments
object 

r1 
a numeric vector of principal components of interest. Choose a subset of r significant PCs to be used. 
r 
a number (a positive integer) of significant principal components. 
s 
a number (a positive integer) of synthetic null variables. Out of m variables, s variables are independently permuted. 
B 
a number (a positive integer) of resampling iterations. There will be a total of s*B null statistics. 
covariate 
a data matrix of covariates with corresponding n observations. 
verbose 
a logical indicator as to whether to print the progress. 
seed 
a seed for the random number generator. 
Details
This function computes m pvalues of linear association between m variables and their PCs. Its resampling strategy accounts for the overfitting characteristics due to direct computation of PCs from the observed data and protects against an anticonservative bias.
Provide the deSet
,
with m variables as rows and n observations as columns. Given that there are
r significant PCs, this function tests for linear association between m
varibles and their r PCs.
You could specify a subset of significant PCs that you are interested in r1. If PC is given, then this function computes statistical significance of association between m variables and PC, while adjusting for other PCs (i.e., significant PCs that are not your interest). For example, if you want to identify variables associated with 1st and 2nd PCs, when your data contains three significant PCs, set r=3 and r1=c(1,2).
Please take a careful look at your data and use appropriate graphical and
statistical criteria to determine a number of significant PCs, r. The number
of significant PCs depends on the data structure and the context. In a case
when you fail to specify r, it will be estimated from a permutation test
(Buja and Eyuboglu, 1992) using a function permutationPA
.
If s is not supplied, s is set to about 10 supplied, B is set to m*10/s.
Value
apply_jackstraw
returns a list
containing the following
slots:
p.value
the m pvalues of association tests between variables and their principal componentsobs.stat
the observed Ftest statisticsnull.stat
the s*B null Ftest statistics
Author(s)
Neo Christopher Chung nc@princeton.edu
References
Chung and Storey (2013) Statistical Significance of Variables Driving Systematic Variation in HighDimensional Data. arXiv:1308.6013 [stat.ME] http://arxiv.org/abs/1308.6013
More information available at http://ncc.name/
See Also
permutationPA
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17  library(splines)
data(kidney)
age < kidney$age
sex < kidney$sex
kidexpr < kidney$kidexpr
cov < data.frame(sex = sex, age = age)
# create models
null_model < ~sex
full_model < ~sex + ns(age, df = 4)
# create deSet object from data
de_obj < build_models(data = kidexpr, cov = cov, null.model = null_model,
full.model = full_model)
## apply the jackstraw
out = apply_jackstraw(de_obj, r1=1, r=1)
## Use optional arguments
## For example, set s and B for a balance between speed of the algorithm and accuracy of pvalues
## out = apply_jackstraw(dat, r1=1, r=1, s=10, B=1000, seed=5678)
