Comments (8)
Neat! Looks straightforward!
from correlation.
From here
ksaai <- function(X, Y, ties = TRUE){
n <- length(X)
r <- rank(Y[order(X)], ties.method = "random")
set.seed(42)
if(ties){
l <- rank(Y[order(X)], ties.method = "max")
return( 1 - n*sum( abs(r[-1] - r[-n]) ) / (2*sum(l*(n - l))) )
} else {
return( 1 - 3 * sum( abs(r[-1] - r[-n]) ) / (n^2 - 1) )
}
}
I don't like that it's not symmetrical - shouldn't correlation coefficients be symmetrical?
x <- rnorm(100, sd = 4)
y <- sin(x) + rnorm(100, sd = 0.2)
plot(x, y)
ksaai(x, y)
#> [1] 0.6306631
ksaai(y, x)
#> [1] -0.1710171
Also the maximal value isn't 1 and seems to depend on the sample size?
z10 <- runif(10)
z100 <- runif(100)
z1000 <- runif(1000)
ksaai(z10, z10)
#> [1] 0.7272727
ksaai(z100, z100)
#> [1] 0.970297
ksaai(z1000, z1000)
#> [1] 0.997003
Created on 2024-04-14 with reprex v2.1.0
from correlation.
Your note about sample size is presumably what he means by "converges to a limit" in point 4 of the screenshot in my original post. Since there's theory to provide confidence intervals, maybe that's not a big deal? Maybe even good?
And on symmetry:
(1) Unlike most coefficients, ξn is not symmetric in X and Y .
But that is intentional. We would like to keep it that way because we may
want to understand if Y is a function X, and not just if one of the variables
is a function of the other. If we want to understand whether X is a function
of Y , we should use ξn(Y, X) instead of ξn(X, Y ). A symmetric measure
of dependence, if required, can be easily obtained by taking the maximum
of ξn(X, Y ) and ξn(Y, X).
from correlation.
Cool (👍
- I don't see any mention of a confidence interval - should we just use Fisher's Z?
- In theory, xi is non-negative, but it sometimes is - should we return 0 in such cases?
from correlation.
I don’t see any mention of a confidence interval
Sorry, I misread about the CI. The XICOR
package does provide a SD, but it feels wrong to just compute a symmetric interval using that.
should we just use Fisher’s Z?
I’ve only really skimmed the paper, and don’t truly understand it. Until I grok this better (realistically: never), I would be reticent to report a quantity not explicitly endorsed by the author.
In theory, xi is non-negative, but it sometimes is - should we return 0 in such cases?
“In the limit” != “In theory”. I’d say report the actual output of the equation, rather than an ad hoc hack.
I ran into some errors with your ksaai()
function with large N. However, the paper authors have published a XICOR
package on CRAN. It seems fast and is published under Apache License which, I believe, is compatible with GPL3.
library(XICOR)
N <- 100
x <- rnorm(N, sd = 4)
y <- sin(x) + rnorm(N, sd = 0.2)
xicor(y, x, pvalue = TRUE)
$xi
[1] 0.03840384
$sd
[1] 0.06325978
$pval
[1] 0.2718984
from correlation.
In theory == I mean the estimand is non-positive.
I'll run some simulations to see if the Fisher Z CIs work well enough.
from correlation.
The author did a small simulation in section 4.2 and concluded that sqrt(n) * xi
is asymptomatically normal (when n = 1000). That's not unexpected, but also not very helpful for more realistic sample sizes.
The author's XICOR package defaults to using the specified mean and SD values with a normal distribution. They also offer a permutation test.
I'd be okay with reporting normal-theory intervals and p values to start given that's what the author does, but we should ideally do some simulations to confirm good performance of the intervals at smaller n (or use a z transform if that works nicely).
I don't compare the code above from the blog post and the XICOR package to be sure they aligned, but we should follow XICOR https://github.com/cran/XICOR/blob/master/R/xicor.R
from correlation.
Hi All,
Just to mention that this preprint has now been published:
Chatterjee, S. (2021). A New Coefficient of Correlation. Journal of the American Statistical Association, 116(536), 2009–2022. https://doi.org/10.1080/01621459.2020.1758115
from correlation.
Related Issues (20)
- Some tests are failing for R < 4.0
- CRAN check failures HOT 3
- Create GitHub release corresponding to CRAN release
- Changing aesthetics of the correlation plot HOT 2
- Costumizing priors HOT 1
- Multilevel correlation changes when more correlations are computed HOT 6
- Suggestion of new function: `cormatrix_to_excel()` HOT 4
- Factors don't always work as intended
- Multilevel rank correlation HOT 1
- refactoring the `correlation` package HOT 6
- Package version doesn't follow easystats' versioning conventions HOT 1
- Bayesian partial correlations
- bayestestR HOT 2
- X
- Update documentation to discuss handling of missing values HOT 1
- specify adjustment variable HOT 1
- Time series auto- and cross-correlations HOT 1
- Expanding Kendall's Tau to include Tau a and Stuart's c
- Update `{correlation}` on CRAN to prevents user from seeing deprecation warnings HOT 5
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