Bootstrap-averaged Chatterjee's xi — xi

Computes Chatterjee's xi B times with random tie-breaking and returns the average. This stabilizes the estimate against tie-breaking variability, which is important for ordinal data with many ties (e.g., Likert-scale items).

Usage

xi_stable(x, y, B = 1000, seed = NULL)

Arguments

x: Numeric or ordered factor (predictor)
y: Numeric or ordered factor (response)
B: Number of bootstrap replications. Default 1000.
seed: Optional integer seed for reproducibility.

Value

A list with elements:

xi: Mean of the B Chatterjee xi values.
sd: Standard deviation of the B values (tie-breaking spread).
se: Standard error of the mean (sd / sqrt(B)).
B: Number of bootstrap replications used.

Details

For each of the B replications, ties in x are broken randomly via rank(x, ties.method = "random") inside chatterjee_xi(). The standard error of the mean shrinks as 1 / sqrt(B); B = 1000 typically yields SE around 0.001 for moderately tied data.

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)
xi_stable(x, y, B = 500, seed = 42)
#> $xi
#> [1] 0.7740774
#> 
#> $sd
#> [1] 0
#> 
#> $se
#> [1] 0
#> 
#> $B
#> [1] 500
#> 
# }