boot.ratio.test: Performs bootstrap ratio test.

Description

Performs bootstrap ratio test which is analogous to a t- or z-score.

Usage

boot.ratio.test(boot.cube, critical.value = 2)

Arguments

boot.cube

an array. This is the bootstrap resampled data. dim 1 (rows) are the items to be tested (e.g., fj, see boot.compute.fj). dim 2 (columns) are the components from the supplemental projection. dim 3 (depth) are each bootstrap sample.

critical.value

numeric. This is the value that would be used as a cutoff in a t- or z-test. Default is 2 (i.e., 1.96 rounded up). The higher the number, the more difficult to reject the null.

Value

A list with the following items: return(list(sig.boot.ratios=significant.boot.ratios,boot.ratios=boot.ratios,critical.value=critical.value))

sig.boot.ratios

This is a matrix with the same number of rows and columns as boot.cube. If TRUE, the bootstrap ratio was larger than critical.value. If FALSE, it was smaller.

boot.ratios

This is a matrix with bootstrap ratio values that has the same number of rows and columns as boot.cube.

critical.value

the critical value input is also returned.

References

The name bootstrap ratio comes from the Partial Least Squares in Neuroimaging literature. See: McIntosh, A. R., & Lobaugh, N. J. (2004). Partial least squares analysis of neuroimaging data: applications and advances. Neuroimage, 23, S250--S263. The bootstrap ratio is related to other tests of values with respect to the bootstrap distribution, such as the Interval-t. See: Chernick, M. R. (2008). Bootstrap methods: A guide for practitioners and researchers (Vol. 619). Wiley-Interscience. Hesterberg, T. (2011). Bootstrap. Wiley Interdisciplinary Reviews: Computational Statistics, 3, 497<U+2013>526.

Examples

Run this code

# NOT RUN {
	##the following code generates 100 bootstrap resampled 
	##projections of the measures from the Iris data set.
	data(ep.iris)
	data <- ep.iris$data
	design <- ep.iris$design
	iris.pca <- epGPCA(data,scale="SS1",DESIGN=design,make_design_nominal=FALSE)
	boot.fjs.unconstrained <- array(0,dim=c(dim(iris.pca$ExPosition.Data$fj),100))
	boot.fjs.constrained <- array(0,dim=c(dim(iris.pca$ExPosition.Data$fj),100))
	for(i in 1:100){
		#unconstrained means we resample any of the 150 flowers
		boot.fjs.unconstrained[,,i] <- boot.compute.fj(ep.iris$data,iris.pca)
		#constrained resamples within each of the 3 groups
		boot.fjs.constrained[,,i] <- boot.compute.fj(data,iris.pca,design,TRUE)		
	}
	#now compute the bootstrap ratios:
	ratios.unconstrained <- boot.ratio.test(boot.fjs.unconstrained)
	ratios.constrained <- boot.ratio.test(boot.fjs.constrained)
# }