Weighted Dependence Measures

Source: R/wdm.R

Computes a (possibly weighted) dependence measure between x and y if these are vectors. If x and y are matrices then the measure between the columns of x and the columns of y are computed.

wdm(x, y = NULL, method = "pearson", weights = NULL, remove_missing = TRUE)

Arguments

x

a numeric vector, matrix or data frame.
y

NULL (default) or a vector, matrix or data frame with compatible dimensions to x. The default is equivalent to `y = x`` (but more efficient).
method

the dependence measure; see Details for possible values.
weights

an optional vector of weights for the observations.
remove_missing

if TRUE, all (pairswise) incomplete observations are removed; if FALSE, the function throws an error if there are incomplete observations.

Details

Available methods:

  • "pearson": Pearson correlation

  • "spearman": Spearman's \(\rho\)

  • "kendall": Kendall's \(\tau\)

  • "blomqvist": Blomqvist's \(\beta\)

  • "hoeffding": Hoeffding's \(D\) Partial matching of method names is enabled.

Spearman's \(\rho\) and Kendall's \(\tau\) are corrected for ties if there are any.

Examples

##  dependence between two vectors
x <- rnorm(100)
y <- rpois(100, 1)  # all but Hoeffding's D can handle ties
w <- runif(100)
wdm(x, y, method = "kendall")               # unweighted
#> [1] -0.007244855
wdm(x, y, method = "kendall", weights = w)  # weighted
#> [1] 0.006367486

##  dependence in a matrix
x <- matrix(rnorm(100 * 3), 100, 3)
wdm(x, method = "spearman")               # unweighted
#>            [,1]       [,2]      [,3]
#> [1,]  1.0000000 -0.1084668 0.1078428
#> [2,] -0.1084668  1.0000000 0.0780318
#> [3,]  0.1078428  0.0780318 1.0000000
wdm(x, method = "spearman", weights = w)  # weighted
#>             [,1]        [,2]      [,3]
#> [1,]  1.00000000 -0.09497972 0.1067206
#> [2,] -0.09497972  1.00000000 0.1292720
#> [3,]  0.10672057  0.12927201 1.0000000

##  dependence between columns of two matrices
y <- matrix(rnorm(100 * 2), 100, 2)
wdm(x, y, method = "hoeffding")               # unweighted
#>              [,1]         [,2]
#> [1,]  0.002148337  0.006288094
#> [2,] -0.002800238 -0.001640325
#> [3,]  0.007099477  0.003868609
wdm(x, y, method = "hoeffding", weights = w)  # weighted
#>              [,1]        [,2]
#> [1,]  0.002481089 0.006531391
#> [2,] -0.004807590 0.001435961
#> [3,]  0.003446762 0.001962314