pdcor {energy}

Partial distance correlation and covariance

Description

Partial distance correlation pdcor, pdcov, and tests.

Usage

  pdcov.test(x, y, z, R)
  pdcor.test(x, y, z, R)
  pdcor(x, y, z)
  pdcov(x, y, z)

Arguments

x

data or dist object of first sample

y

data or dist object of second sample

z

data or dist object of third sample

R

replicates for permutation test

Details

pdcor(x, y, z) and pdcov(x, y, z) compute the partial distance correlation and partial distance covariance, respectively, of x and y removing z.

A test for zero partial distance correlation (or zero partial distance covariance) is implemented in pdcor.test, and pdcov.test.

Argument types supported are numeric data matrix, data.frame, tibble, numeric vector, class "dist" object, or factor. For unordered factors a 0-1 distance matrix is computed.

Value

Each test returns an object of class htest.

Author(s)

Maria L. Rizzo [e-mail] and Gabor J. Szekely

References

Szekely, G.J. and Rizzo, M.L. (2014), Partial Distance Correlation with Methods for Dissimilarities. Annals of Statistics, Vol. 42 No. 6, 2382-2412.

Examples

  n = 30
  R <- 199

  ## mutually independent standard normal vectors
  x <- rnorm(n)
  y <- rnorm(n)
  z <- rnorm(n)

  pdcor(x, y, z)
  pdcov(x, y, z)
  set.seed(1)
  pdcov.test(x, y, z, R=R)
  set.seed(1)
  pdcor.test(x, y, z, R=R)


  if (require(MASS)) {
    p = 4
    mu <- rep(0, p)
    Sigma <- diag(p)
  
    ## linear dependence
    y <- mvrnorm(n, mu, Sigma) + x
    print(pdcov.test(x, y, z, R=R))
  
    ## non-linear dependence
    y <- mvrnorm(n, mu, Sigma) * x
    print(pdcov.test(x, y, z, R=R))
    }