rococo {rococo}

Robust Gamma Rank Correlation Coefficient

Description

Compute the robust gamma rank correlation coefficient

Usage

rococo(x, y,
       similarity=c("linear", "exp", "gauss", "epstol", "classical"),
       tnorm="min", r=0, noVarReturnZero=TRUE)

Arguments

x

a numeric vector; compulsory argument

y

a numeric vector; compulsory argument; x and y need to have the same length

similarity

a character string or a character vector identifying which type of similarity measure to use; valid values are "linear" (default), "exp", "gauss", "epstol", and "classical" (abbreviations are allowed as long as they are unique). If similarity is a single string, the same similarity measure is taken for x and y. Different similarity measures can be used for x and y by supplying different similarity measures in similarity[1] and similarity[2]. Longer character vectors are allowed, but all but the first two entries are ignored.

tnorm

can be any of the following strings identifying a standard tnorm: "min" (minimum t-norm; default), "prod" (product t-norm), or lukasiewicz (Lukasiewicz t-norm); abbreviations are allowed as long as they are unique. Alternatively, tnorm can be a two-argument function defining a t-norm.

r

numeric vector defining the tolerances to be used; if a single value is supplied, the same value is used both for x and y. If a vector is supplied, r[1] is used as tolerance for x and r[2] is used as tolerance for y. If the classical crisp similarity is used, the corresponding entry/entries in r is/are ignored. Negative values are not allowed. Zeroes have a special meaning: if an entry in r is 0, then the tolerance is automatically adapted to 10 percent of the interquartile range of the data.

noVarReturnZero

if TRUE (default), a correlation of 0 is returned if there is no variation in at least one of the two observables. Otherwise, NA is returned and a warning is issued.

Details

rococo computes the robust gamma rank correlation coefficient of x and y according to the specified parameters (see literature for more details).

Note that rococo only works for x and y being numeric vectors, unlike the classical correlation measures implemented in cor which can also be computed for matrices or data frames.

Value

Upon successful completion, the function returns the robust gamma rank correlation coefficient.

Author(s)

Martin Krone and Ulrich Bodenhofer

References

https://github.com/UBod/rococo

U. Bodenhofer and F. Klawonn (2008). Robust rank correlation coefficients on the basis of fuzzy orderings: initial steps. Mathware Soft Comput. 15(1):5-20.

U. Bodenhofer, M. Krone, and F. Klawonn (2013). Testing noisy numerical data for monotonic association. Inform. Sci. 245:21-37. DOI: doi:10.1016/j.ins.2012.11.026.

See Also

rococo.test

Examples

## create data
f <- function(x) ifelse(x > 0.9, x - 0.9, ifelse(x < -0.9, x + 0.9, 0))
x <- rnorm(25)
y <- f(x) + rnorm(25, sd=0.1)

## compute correlation
rococo(x, y, similarity="classical")
rococo(x, y, similarity="linear")
rococo(x, y, similarity=c("classical", "gauss"), r=c(0, 0.1))