getNormalizer {shuffle}

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.

Details

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

Author(s)

Yuval Benjamini

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))