Computes Chatterjee's (2021) rank-based correlation coefficient xi.
Unlike Pearson or Spearman, xi is asymmetric: xi(x, y) and xi(y, x)
may differ. This asymmetry is the basis for direction-detection in
graphical models.
Usage
chatterjee_xi(x, y, ties_method = "random")
Arguments
- x
Numeric or ordered factor (predictor)
- y
Numeric or ordered factor (response)
- ties_method
How to break ties in x. Default "random".
Value
Numeric scalar: Chatterjee's xi value.
Details
For tied x values, ranks are broken using ties_method. With
"random" (the default), each call may produce a slightly
different value due to random tie-breaking. Use xi_stable()
to average over many randomizations.
References
Chatterjee, S. (2021). A new coefficient of correlation. Journal of
the American Statistical Association, 116(536), 2009-2022.
Examples
# \donttest{
x <- rnorm(100)
y <- x^2 + rnorm(100, sd = 0.1)
chatterjee_xi(x, y) # near 1, since y is determined by x
#> [1] 0.7008701
chatterjee_xi(y, x) # smaller, since x is not determined by y
#> [1] 0.289529
# }
