README.md

In JonasMoss/rankr: Estimation and inference for variants of Kendall's tau

rankr

An R package for calculating varieties of Kendall’s tau in O(nlog(n)) time. Bias-corrected accelerated bootstrap[^1] supported. Designed to facilitate the computation of the new tau varieties in Moss (2024, WIP), but supports most variants of tau in the literature.

Work in progress! Analytical confidence intervals hopefully coming soon, along with a preprint describing the new variants of tau and their rationale. Expect breaking changes to the API.

Installation

You can install the development version of rankr from GitHub with:

# install.packages("remotes")
remotes::install_github("JonasMoss/rankr")

Example

The cylinder covariate in the mtcars is almost a weakly decreasing function of the miles per gallon covariate. On the other hand, miles per gallon is not a monotone function of cylinder:

par(mfrow=c(1,2))
plot(mtcars$mpg, mtcars$cyl, xlab = "Miles per gallon", ylab = "Cylinders")
plot(mtcars$cyl, mtcars$mpg, xlab = "Cyliders", ylab = "Miles per gallon")

The rankr package supports caclulation of several variants of Kendall’s tau. Most importantly, it supports the weakly monotone tau (Moss, 2024).

library("rankr")
c(tau(mtcars$mpg, mtcars$cyl), tau(mtcars$cyl, mtcars$mpg))
#> [1] -0.9819005 -0.3399602

Both numbers are negative, implying the best-fitting monotone function is decreasing. The first number is almost -1, implying that cyl is almost perfectly a weakly decreasing function of mpg. The second number is merely -0.34, implying there is only a weak monotone functional relationship mpg = f(cyl).

Calculate approximate confidence intervals using the bias-corrected and accelerated bootstrap (BCa):

set.seed(313)
tau_ci(mtcars$mpg, mtcars$cyl, "tau")
#>      0.025      0.975 
#> -0.9971223 -0.8999599
tau_ci(mtcars$cyl, mtcars$mpg, "tau")
#>      0.025      0.975 
#> -0.4203455 -0.1149544

Additional functionality

Most variants of tau in the literature can be calculated by rankr. All computations are O(nlog(n)).

| | Function | cyl ~ mpg | mpg ~ cyl | Symmetric? | |:---------------------------|:-------------|:----------|:----------|:-----------| | Generalized tau[^2] | tau | -0.982 | -0.34 | 𐄂 | | Strict generalized tau[^3] | tau_strict | -0.493 | -0.643 | 𐄂 | | Kendall’s tau (a)[^4] | tau_a | -0.643 | -0.643 | 🗸 | | Kendall’s tau (b)[^5] | tau_b | -0.795 | -0.795 | 🗸 | | Stuart’s tau (c)[^6] | tau_c | -0.935 | -0.935 | 🗸 | | Goodman–Kruskall gamma[^7] | gk_gamma | -0.976 | -0.976 | 🗸 | | Somer’s D[^8] | somers_d | -0.97 | -0.652 | 𐄂 | | Wilson’s E[^9] | wilsons_e | -0.65 | -0.65 | 🗸 | | Leik–Gove D[^10] | lg_d | -0.964 | -0.49 | 𐄂 |

[^1]: Efron, B. (1987). Better Bootstrap Confidence Intervals. Journal of the American Statistical Association, 82(397), 171–185. https://doi.org/10.2307/2289144

[^2]: Moss, J. (2024). Kendall’s tau and proportional reduction in risk: New generalizations for tied data (WIP)

[^3]: Moss, J. (2024). Kendall’s tau and proportional reduction in risk: New generalizations for tied data (WIP)

[^4]: Kendall, M. G. (1938). A New Measure of Rank Correlation. Biometrika, 30(1/2), 81–93. https://doi.org/10.2307/2332226

[^5]: Kendall, M. G. (1945). The treatment of ties in ranking problems. Biometrika, 33, 239–251. https://doi.org/10.1093/biomet/33.3.239

[^6]: Stuart, A. (1953). The Estimation and Comparison of Strengths of Association in Contingency Tables. Biometrika, 40(1/2), 105–110. https://doi.org/10.2307/2333101

[^7]: Somers, R. H. (1962). A New Asymmetric Measure of Association for Ordinal Variables. American Sociological Review, 27(6), 799–811. https://doi.org/10.2307/2090408

[^8]: Goodman, L. A., & Kruskal, W. H. (1979). Measures of Association for Cross Classifications. In L. A. Goodman & W. H. Kruskal (Eds.), Measures of Association for Cross Classifications (pp. 2–34). Springer New York. https://doi.org/10.1007/978-1-4612-9995-0_1

[^9]: Wilson, T. P. (1974). Measures of association for bivariate ordinal hypotheses. In H. Blalock (Ed.), Measurement in the Social Sciences. Taylor Francis. https://doi.org/10.4324/9781351329088-14

[^10]: Leik, R. K., & Gove, W. R. (1969). The Conception and Measurement of Asymmetric Monotonic Relationships in Sociology. The American Journal of Sociology, 74(6), 696–709. https://doi.org/10.1086/224720

JonasMoss/rankr documentation built on Feb. 5, 2024, 11:56 a.m.