shuffle (version 1.0.1)

getNormalizer: getNormalizer

Description

Computes the normalizer 1/(1-alpha) for a given design and permutation. The shuffle estimator is [MSbet(Y) - MSbet(PY)]*normalizer. \ We prefer the normalizer to be close to 1.

Usage

getNormalizer(avgmat, perm)

Arguments

avgmat

The output of getAveraging.

perm

The shuffling permutation.

Value

norm

The value by which to correct the difference of variances [1/(facA-facB)]

facA

The signal coefficient of the original design, should be 1

facB

The signal variance coefficient of the permuted design

Details

Under balanced designs, the normalizer = 1/[1-alpha]. More generally, we call facA = 1 and facB = alpha(design, permutation).

References

Benjamini and Yu (2013).

Examples

data(design_vec)

# Make example shorter - for paper example use T = ncol(fMRI_responses) = 156*10
T = 156*4
design_sm = design_vec[1:T]

identity_perm = 1:T
reverse_perm = rev(identity_perm)
shift_perm = c(2:T, 1)

design_avg = getAveraging(design_sm)
identity_norm = getNormalizer(design_avg, identity_perm)
print('For the identity, we cannot get an estimator')
print(sprintf('facA(1) %.3f, facB(alpha) %.3f, normalizer %.3f ', 
		    identity_norm$facA, identity_norm$facB, identity_norm$norm))

reverse_norm = getNormalizer(design_avg, reverse_perm)
print('For the reverse, we get a normalizer close to 1 ')
print(sprintf('facA(1) %.3f, facB(alpha) %.3f, normalizer %.3f ', 
		    reverse_norm$facA, reverse_norm$facB, reverse_norm$norm))

shift_norm = getNormalizer(design_avg, shift_perm)
print('The shift mixes across blocks. The normalizer is smaller, but assumptions may not hold')
print(sprintf('facA(1) %.3f, facB(alpha) %.3f, normalizer %.3f ', 
		    shift_norm$facA, shift_norm$facB, shift_norm$norm))