perm.jntrank {CJIVE}

Permutation Test for Joint Rank in CJIVE

Description

Conducts the permutation test for the number of joint components as described in CJIVE manuscript. Briefly, canonical correlations (CC) between principal component vectors of the data are obtained (PC). Then for 1:nperms, the rows of one data set are permuted and CCs between PC vectors are calculated, retaining the maximum CC. These maximum CCs form a null distribution against which the original CCs are tested. The number of original CCs exceeding the (1-alpha)^th percentile is the returned as the joint rank.

Usage

perm.jntrank(
  dat.blocks,
  signal.ranks = NULL,
  nperms = 500,
  perc.var = 0.95,
  alpha = 0.05,
  center = TRUE
)

Arguments

dat.blocks

a list of two matrices with samples along rows and features along columns, which contain data on the same n individuals/sampling units

signal.ranks

a vector of length two which contains the rank for the signal within each data block. The rank corresponds to the number of principal components (PCs) to be retained within each data block. If NULL, the ranks are determined by the parameter 'perc.var.' Default is NULL

nperms

integer value indicating the number of permutations that should be performed

perc.var

numeric value of either a scalar or of length 2: an alternative to signal.ranks that allows specification of signal ranks based on the desired proportion of total variation to be retained in each data block. For perc.var = p (where 0<p<1), rank is determined as the minimum number of eigenvalues whose cumulative sum is at least p*(total sum of eigenvalues). Default is 0.95 (i.e. 95% of total variation preserved for each data block). For p=c(p1,p2) pk is used to determine the rank of block k

alpha

nominal type-I error rate

center

logical (TRUE/FALSE) indicating whether data should be column-centered prior to testing. Default is TRUE

Value

The Frobenius norm of the matrix X, calculated as the sum of square entries in X