Addition of WMWodds (wmw_odds function)

[arcaldwell49]

Description

This PR aims at adding WMWodds (Agresti's Generalized Odds Ratio) to the rank based effect sizes. Using the odds_to_probs function, the output can be considered a concordance probability or a non-parametric probability of superiority.

Proposed Changes

I created the wmw_odds function which effectively mimics rank_biserial but instead calculates the odds. Tests and vignettes have also been added.

[arcaldwell49]

Conflicts will need to be resolved, but all changes to files other than rank_effectisizes.R, man/rank_biserial.Rd, and tests/testthat/test-rankES.R can be ignored or ditched.

[mattansb]

I'm reading the docs, and it seems like this function would be better suited under the common-language effect sizes.

Also, it seems like this function produces the same results are rank_biserial() |> rb_to_cles() |> probs_to_odds() (with or without ties) with CIs from wmw_odds() being slightly (?) more conservative.

library(effectsize)

p <- rb_to_cles(rank_biserial(mpg ~ am, data = mtcars))
p[c(2, 4:5)] <- lapply(p[c(2, 4:5)], probs_to_odds)
colnames(p)[2] <- "odds"
p[-1]
#> odds |       95% CI
#> -------------------
#> 0.20 | [0.09, 0.47]

# The same...?
wmw_odds(mpg ~ am, data = mtcars)
#> odds |       95% CI
#> -------------------
#> 0.20 | [0.07, 0.58]





x <- c(1.83,  0.50,  1.62,  2.48, 1.68, 1.88, 1.55, 3.06, 1.30)
y <- c(0.878, 0.647, 0.598, 2.05, 1.06, 1.29, 1.06, 3.14, 1.29)

p <- rb_to_cles(rank_biserial(x, y))
p[c(2, 4:5)] <- lapply(p[c(2, 4:5)], probs_to_odds)
colnames(p)[2] <- "odds"
p[-1]
#> odds |       95% CI
#> -------------------
#> 2.52 | [0.84, 7.55]

# The same...?
wmw_odds(x, y)
#> odds |       95% CI
#> -------------------
#> 2.52 | [0.66, 9.61]




p <- rb_to_cles(rank_biserial(cyl ~ am, data = mtcars))
p[c(2, 4:5)] <- lapply(p[c(2, 4:5)], probs_to_odds)
colnames(p)[2] <- "odds"
p[-1]
#> odds |       95% CI
#> -------------------
#> 3.66 | [1.60, 8.37]

# The same...?
wmw_odds(cyl ~ am, data = mtcars)
#> odds |       95% CI
#> -------------------
#> 3.66 | [1.48, 9.07]

^{Created on 2022-09-24 by the reprex package (v2.0.1)}

So unless there is a reason not to use rank_biserial() |> rb_to_cles() |> probs_to_odds(), I think we should go forward with this instead (sorry for all your hard work!)

[arcaldwell49]

Okay, I have two reasons.

1. The coverage of confidence intervals for the rank_biserial() |> rb_to_cles() |> probs_to_odds() is quite poor IMO. I ran a short set of simulations for the Fisher r-to-z for WMWodds and coverage is not adequate even under the null hypothesis. The Agresti normal approximation I have written is still quite liberal when the effect size is large (odd < .75 and odds > 1.5 respectively), but certainly performs better than the Fisher transform approach.

2. wmw_odds has an option for paired samples. Currently, the cles function does not allow for paired samples comparisons. Now, I will admit the confidence intervals for this method are very conservative.

For example:

> cles(extra ~ group, data = sleep, parametric = FALSE, paired = TRUE)
Error in rank_biserial(x = x, y = y, paired = FALSE, mu = mu, ci = ci,  : 
  formal argument "paired" matched by multiple actual arguments

> wmw_odds(extra ~ group, data = sleep, parametric = FALSE, paired = TRUE)
odds |       95% CI
-------------------
0.05 | [0.01, 0.53]

rank_biserial(extra ~ group, data = sleep, parametric = FALSE, paired = TRUE) |> rb_to_cles() |> probs_to_odds(
+ )
 Error: Common language effect size only applicable to 2-sample rank-biserial correlation.

It's totally up to you and your team, but as a user of effectsize, I would really like this function 😓

Happy to convert this over to cles if you want to reconsider its inclusion!

[mattansb]

Here's what I suggest:

1. Add this function to CLES using the transformations I noted above

2. Open a new issue / pr to discuss improving the CI covered for all of these methods - since they are all monotonic transformations of one another, it makes sense to me they can be improved together.

[arcaldwell49]

Ok, I will get on that shortly and thank you!

I will close this pull request and start working on the CLES improvements.