population2sample.test {BrainCon}

Identify differences of partial correlations between two populations

Description

Identify differences of partial correlations between two populations in two groups of time series data by controlling the rate of the false discovery proportion (FDP) exceeding c0 at \alpha, considering time dependence. Input two popEst class objects returned by population.est (the number of individuals in two groups can be different).

Usage

population2sample.test(
  popEst1,
  popEst2,
  alpha = 0.05,
  c0 = 0.1,
  targetSet = NULL,
  MBT = 5000,
  simplify = !is.null(targetSet)
)

Arguments

popEst1

A popEst class object.

popEst2

A popEst class object.

alpha

significance level, default value is 0.05.

c0

threshold of the exceedance rate of FDP, default value is 0.1. A smaller value of c0 will reduce false positives, but it may also cost more false negatives.

targetSet

a two-column matrix. Each row contains two index corresponding to a pair of variables of interest. If NULL, any pair of two variables is considered to be of interest.

MBT

times of multiplier bootstrap, default value is 5000.

simplify

a logical indicating whether results should be simplified if possible.

Value

If simplify is FALSE, a p*p matrix with values 0 or 1 is returned. If the j-th row and k-th column of the matrix is 1, then the partial correlation coefficients between the j-th variable and the k-th variable in two populations are identified to be unequal.

And if simplify is TRUE, a two-column matrix is returned, indicating the row index and the column index of recovered unequal partial correlations. We only retain the results which the row index is less than the column index. Those with larger test statistics are sorted first.

References

Qiu Y. and Zhou X. (2021). Inference on multi-level partial correlations based on multi-subject time series data, Journal of the American Statistical Association, 00, 1-15.

Examples

## Quick example for the two-sample case inference
data(popsimA)
data(popsimB)
# estimating partial correlation coefficients by lasso (scaled lasso does the same)
pc1 = population.est(popsimA, type = 'l')
pc2 = population.est(popsimB, type = 'l')
# conducting hypothesis test
Res = population2sample.test(pc1, pc2)
# conducting hypothesis test and returning simplified results
Res_s = population2sample.test(pc1, pc2, simplify = TRUE)