Partial distance correlation and covariance

Partial distance correlation pdcor, pdcov, and tests.

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

Maria L. Rizzo mrizzo@bgsu.edu 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)
#>      pdcor 
#> 0.03256314 
  pdcov(x, y, z)
#> [1] 0.01237857
  set.seed(1)
  pdcov.test(x, y, z, R=R)
#> 
#> 	pdcov test
#> 
#> data:  replicates 199
#> n V^* = 0.37136, p-value = 0.105
#> sample estimates:
#>      pdcor 
#> 0.03256314 
#> 
  set.seed(1)
  pdcor.test(x, y, z, R=R)
#> 
#> 	pdcor test
#> 
#> data:  replicates 199
#> pdcor = 0.032563, p-value = 0.105
#> sample estimates:
#>      pdcor 
#> 0.03256314 
#> 

# \donttest{
  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))
    }
#> 
#> 	pdcov test
#> 
#> data:  replicates 199
#> n V^* = 18.664, p-value = 0.005
#> sample estimates:
#>     pdcor 
#> 0.7661325 
#> 
#> 
#> 	pdcov test
#> 
#> data:  replicates 199
#> n V^* = 0.44957, p-value = 0.165
#> sample estimates:
#>      pdcor 
#> 0.04511353 
#> 
  # }