Weighted Dependence Measures

Provides efficient implementations of weighted dependence measures and related asymptotic tests for independence. Implemented measures are the Pearson correlation, Spearman's rho, Kendall's tau, Blomqvist's beta, Hoeffding's D, and Chatterjee's xi; see, e.g., Nelsen (2006) , Hollander et al. (2015, ISBN:9780470387375), and Chatterjee (2021) .

output: github_document

wdm

CRAN downloads

R interface to the wdm C++ library, which provides efficient implementations of weighted dependence measures and related independence tests:

Pearson's rho
Spearman's rho
Kendall's tau
Blomqvist's beta
Hoeffding's D
Chatterjee's xi

All measures are computed in O(n log n) time, where n is the number of observations.

For a detailed description of the functionality, see the API documentation.

Installation

the stable release from CRAN:

install.packages("wdm")

the development version from GitHub with:

# install.packages("devtools")
install_submodule_git <- function(x, ...) {
  install_dir <- tempfile()
  system(paste("git clone --recursive", shQuote(x), shQuote(install_dir)))
  devtools::install(install_dir, ...)
}
install_submodule_git("https://github.com/tnagler/wdm-r")

Cloning

This repo contains wdm as a submodule. For a full clone use

git clone --recurse-submodules <repo-address>

Examples

library(wdm)

Dependence between two vectors

x <- rnorm(100)
y <- rpois(100, 1)
w <- runif(100)
wdm(x, y, method = "kendall")               # unweighted
#> [1] 0.04547414
wdm(x, y, method = "kendall", weights = w)  # weighted
#> [1] 0.07764891

Dependence in a matrix

x <- matrix(rnorm(100 * 3), 100, 3)
wdm(x, method = "spearman")               # unweighted
#>             [,1]        [,2]        [,3]
#> [1,]  1.00000000  0.10045005 -0.03279928
#> [2,]  0.10045005  1.00000000 -0.02744674
#> [3,] -0.03279928 -0.02744674  1.00000000
wdm(x, method = "spearman", weights = w)  # weighted
#>             [,1]       [,2]        [,3]
#> [1,]  1.00000000 0.22080359 -0.05369922
#> [2,]  0.22080359 1.00000000  0.01192067
#> [3,] -0.05369922 0.01192067  1.00000000

Chatterjee's xi measures the dependence of the second argument on the first, so reversing the arguments can change the result:

wdm(x[, 1], x[, 2], method = "chatterjee")
#> [1] 0.01740174
wdm(x[, 2], x[, 1], method = "chatterjee")
#> [1] 0.03510351

Independence test

x <- rnorm(100)
y <- rpois(100, 1)
w <- runif(100)
indep_test(x, y, method = "kendall")               # unweighted
#>     estimate statistic   p_value n_eff  method alternative
#> 1 0.02140979 0.2799245 0.7795354   100 kendall   two-sided
indep_test(x, y, method = "kendall", weights = w)  # weighted
#>     estimate statistic   p_value   n_eff  method alternative
#> 1 0.04616801 0.5015067 0.6160145 71.2503 kendall   two-sided

For Chatterjee's xi, x is the predictor and y is the response. Its natural one-sided alternative is "greater":

indep_test(x, y, method = "chatterjee", alternative = "greater")
#>      estimate statistic   p_value n_eff     method alternative
#> 1 -0.04496517 -0.576012 0.7176965   100 chatterjee     greater