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Calculate rank scores

Source: R/CMRSS_CRE.R
rank_score.Rd

Computes rank scores for rank-based test statistics. Supports Wilcoxon, Stephenson, and Polynomial rank scores.

Usage

rank_score(
  n,
  method.list = list(name = "Polynomial", r, std = TRUE, scale = FALSE)
)

Arguments

n

Number of units.

method.list

A list specifying the scoring method:

  • name: "Wilcoxon", "Stephenson", or "Polynomial"

  • s: (for Stephenson) the parameter s

  • divide_by_top: (for Stephenson) logical. TRUE, and also when left out, divides every score by the top unit's score choose(n - 1, s - 1), so scores run from 0 to 1. FALSE gives the binomial coefficients choose(r - 1, s - 1) themselves.

  • r: (for Polynomial) the power parameter

  • std: (for Polynomial) logical, use Puri(1965) normalization

  • scale: logical, standardize scores to mean 0 and sd 1

Value

A numeric vector of length n containing the rank scores.

Details

Polynomial scores optionally use Puri(1965) normalization. Stephenson scores use binomial coefficients, by default divided by the top unit's score. The division is computed on the log scale, exp(lchoose(r - 1, s - 1) - lchoose(n - 1, s - 1)), because the coefficients themselves exceed the largest double once they pass about 1e308: with s = 500, from n = 1,032 on, where the undivided scores are Inf and every p-value is NA. Without strata the division changes no p-value, since the observed statistic and every null draw are multiplied by the same constant. With strata of unequal size it changes the test, because each stratum's scores are divided by a different number: undivided, a stratum of 100 with s = 10 has top score choose(99, 9) = 1.7e12 and a stratum of 20 has choose(19, 9) = 92,378, so the larger stratum carries nearly all the weight. Wilcoxon scores are simply the ranks 1 to n.

Examples

rank_score(5, list(name = "Wilcoxon", scale = FALSE))
#> [1] 1 2 3 4 5
rank_score(5, list(name = "Stephenson", s = 3, scale = FALSE))
#> [1] 0.0000000 0.0000000 0.1666667 0.5000000 1.0000000
rank_score(5, list(name = "Stephenson", s = 3, divide_by_top = FALSE, scale = FALSE))
#> [1] 0 0 1 3 6
rank_score(5, list(name = "Polynomial", r = 2, std = TRUE, scale = FALSE))
#> [1] 0.1666667 0.3333333 0.5000000 0.6666667 0.8333333