xicor: Compute the cross rank increment correlation coefficient xi.

In XICOR: Association Measurement Through Cross Rank Increments

Compute the cross rank increment correlation coefficient xi.

Description

This function computes the xi coefficient between two vectors x and y, possibly all coefficients for a matrix. If only one coefficient is computed it can be used to test independence using a Monte Carlo permutation test or through an asymptotic approximation test.

Usage

xicor(
  x,
  y = NULL,
  pvalue = FALSE,
  ties = TRUE,
  method = "asymptotic",
  nperm = 1000,
  factor = FALSE
)

Arguments

x	Vector of numeric values in the first coordinate.
y	Vector of numeric values in the second coordinate.
pvalue	Whether or not to return the p-value of rejecting independence, if TRUE the function also returns the standard deviation of xi.
ties	Do we need to handle ties? If ties=TRUE the algorithm assumes that the data has ties and employs the more elaborated theory for calculating s.d. and P-value. Otherwise, it uses the simpler theory. There is no harm in putting ties = TRUE even if there are no ties.
method	If method = "asymptotic" the function returns P-values computed by the asymptotic theory. If method = "permutation", a permutation test with nperm permutations is employed to estimate the P-value. Usually, there is no need for the permutation test. The asymptotic theory is good enough.
nperm	In the case of a permutation test, nperm is the number of permutations to do.
factor	Whether to transform integers into factors, the default is to leave them alone.

Value

In the case pvalue=FALSE, function returns the value of the xi coefficient, if the input is a matrix, a matrix of coefficients is returned. In the case pvalue=TRUE is chosen, the function returns a list:

xi

The value of the xi coefficient.

sd

The standard deviation.

pval

The test p-value.

Note

Dataset peas no longer available in psych, we are now using psychTools.

This version does not use a seed as argument, if reproducibility is an issue, set a seed before calling the function.

Author(s)

Sourav Chatterjee, Susan Holmes

References

Chatterjee, S. (2020) <arXiv:1909.10140>.

See Also

dcov

Examples

##---- Should be DIRECTLY executable !! ----
library("psychTools")
data(peas)
# Visualize       the peas data
library(ggplot2)
ggplot(peas,aes(parent,child)) +
geom_count() + scale_radius(range=c(0,5)) +
       xlim(c(13.5,24))+ylim(c(13.5,24))+       coord_fixed() +
       theme(legend.position="bottom")
# Compute one of the coefficients
xicor(peas$parent,peas$child,pvalue=TRUE)
xicor(peas$child,peas$parent)
# Compute all the coefficients
xicor(peas)

XICOR documentation built on April 21, 2023, 5:06 p.m.