Package 'rococo'

Gauss Rank Correlation Estimator

Description

Compute the Gaussian rank correlation estimate

Usage

gauss.cor(x, y)

Arguments

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

Details

gauss.cor computes the Gaussian rank correlation estimate for x and y.

Note that gauss.cor 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 Gaussian rank correlation estimate.

Author(s)

Ulrich Bodenhofer

References

https://github.com/UBod/rococo

K. Boudt, J. Cornelissen, and C. Croux (2012). The Gaussian rank correlation estimator: robustness properties. Stat. Comput. 22(2):471-483. DOI: doi:10.1007/s11222-011-9237-0.

See Also

gauss.cor.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
gauss.cor(x, y)

---

Gaussian rank correlation test

Description

Methods performing a Gaussian rank correlation test

Usage

## S4 method for signature 'numeric,numeric'
gauss.cor.test(x, y, ...)
## S4 method for signature 'formula,data.frame'
gauss.cor.test(x, y, na.action, ...)

Arguments

x	a numeric vector or a formula; compulsory argument
y	compulsory argument; if x is a vector, y must be vector of the same length as x. If x is a formula, y must be a data frame.
na.action	a function which indicates what should happen when the data contain NA's. Defaults to getOption("na.action").
...	all parameters specified are forwarded internally to the method cor.test, in particular, the alternative parameter.

Details

If called for numeric vectors, gauss.cor.test performs the Gaussian gamma rank correlation test for x and y. This is done by simply performing a Pearson correlation test on the normal scores of the data.

If gauss.cor.test is called for a formula x and a data frame y, then the method checks whether the formula x correctly extracts two columns from y (see examples below). If so, the two columns are extracted and the Gaussian gamma rank correlation test is applied to them according to the specified parameters.

Value

Upon successful completion, the function returns a list of class htest containing the results (see cor.test).

Author(s)

Ulrich Bodenhofer

References

https://github.com/UBod/rococo

K. Boudt, J. Cornelissen, and C. Croux (2012). The Gaussian rank correlation estimator: robustness properties. Stat. Comput. 22(2):471-483. DOI: doi:10.1007/s11222-011-9237-0.

See Also

gauss.cor

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)

## perform correlation tests
gauss.cor.test(x, y, alternative="greater")

## the formula variant
require(datasets)
data(iris)
gauss.cor.test(~ Petal.Width + Petal.Length, iris,
               alternative="two.sided")

---

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))

---

Robust Gamma Rank Correlation Test

Description

Methods performing a robust gamma rank correlation test

Usage

## S4 method for signature 'numeric,numeric'
rococo.test(x, y,
            similarity=c("linear", "exp", "gauss",
                         "epstol", "classical"),
            tnorm="min", r=0, numtests=1000, storeValues=FALSE,
            exact=FALSE, alternative=c("two.sided", "less", "greater"),
            noVarReturnZero=TRUE)
## S4 method for signature 'formula,data.frame'
rococo.test(x, y, na.action, ...)

Arguments

x	a numeric vector or a formula; compulsory argument
y	compulsory argument; if x is a vector, y must be vector of the same length as x. If x is a formula, y must be a data frame.
similarity	a character string or a character vector identifying which type of similarity measure to use; see rococo for more details.
tnorm	t-norm used for aggregating results; see rococo for more details.
r	numeric vector defining the tolerances to be used; see rococo for more details.
numtests	number of random shuffles to perform; see details below.
storeValues	logical indicating whether the vector of test statistics should be stored in the output object (in slot perm.gamma, see RococoTestResults).
exact	logical indicating whether exact p-value should be computed; see details below.
alternative	indicates the alternative hypothesis and must be one of "two.sided", "greater", or "less". Abbreviations are allowed as long as they are unique. "greater" corresponds to positive association, "less" to negative association.
noVarReturnZero	if TRUE (default), a correlation of 0 and a p-value of 1 are returned if there is no variation in at least one of the two observables. Otherwise, a correlation of NA and a p-value of 1 are returned and a warning is issued.
na.action	a function which indicates what should happen when the data contain NA's. Defaults to getOption("na.action").
...	all parameters specified are forwarded internally to the method rococo.test with signature numeric,numeric.

Details

If called for numeric vectors, rococo.test computes the robust gamma rank correlation coefficient of x and y according to the specified parameters (see rococo) and then performs a permutation test to compute a p-value. If exact=TRUE, rococo.test attempts to compute an exact p-value and ignores the numtests argument. This is done by considering all possible permutations and computing the ratio of permutations for which the test statistic is at least as large/small as the test statistic for unshuffled data. This works only for 10 or less samples. Otherwise exact=TRUE is ignored, a warning is issued and random shuffles are considered to estimate the p-value (as follows next). If exact=FALSE, numtests random shuffles of y are performed and the empirical standard deviation of the robust gamma correlation values for these shuffled data sets is computed. Under the assumption that these values are normally distributed around mean zero, the p-value is then computed from this distribution in the usual way. Note that a too small choice of the number of shuffles (parameter numtests) leads to unreliable p-values.

If rococo.test is called for a formula x and a data frame y, then the method checks whether the formula x correctly extracts two columns from y (see examples below). If so, the two columns are extracted and the robust gamma rank correlation test is applied to them according to the specified parameters.

Note that exact=TRUE may result in long computation times for user-defined t-norms.

Value

Upon successful completion, the function returns an object of class RococoTestResults containing the results.

Author(s)

Martin Krone and Ulrich Bodenhofer

References

https://github.com/UBod/rococo

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.

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.

See Also

rococo

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)

## perform correlation tests
rococo.test(x, y, similarity="classical", alternative="greater")
rococo.test(x, y, similarity="linear", alternative="greater")
rococo.test(x, y, similarity=c("classical", "gauss"), r=c(0, 0.1),
            alternative="greater", numtests=10000)

## the formula variant
require(datasets)
data(iris)
rococo.test(~ Petal.Width + Petal.Length, iris, similarity="linear",
            alternative="two.sided")

---

Class "RococoTestResults"

Description

S4 class for storing results of the robust rank correlation test

Objects

Objects of this class can be created by calling rococo.test.

Slots

The following slots are defined for RococoTestResults objects:

count:

number of times in which the test statistic for a random shuffle exceeded the test statistic of the true data; see rococo.test.

tnorm:

list identifying t-norm to use or two-argument function; see rococo. If one of the standard choices "min", "prod", or "lukasiewicz" has been used, the list has one component, name that contains the string identifying the t-norm. If a user-defined function has been used, the list has two components: name contains "user-defined t-norm" or the name attribute of the function object if available and def contains the function object itself.

input:

character string describing the input for which rococo.test has been called.

length:

number of samples for which rococo.test has been called.

p.value:

p-value of test.

p.value.approx:

p-value as based on a normal approximation of the null distribution.

r.values:

vector containing tolerance levels for the two inputs; see rococo.test or rococo.

numtests:

number of (random) shuffles performed by rococo.test.

exact:

logical indicating whether p-value has been computed exactly; see rococo.test.

similarity:

character (vector) identifying the similarity measure(s) used by rococo.test.

sample.gamma:

test statistic (robust gamma rank correlation coefficient) determined by rococo.test.

H0gamma.mu:

empirical mean of test statistic for random shuffles

H0gamma.sd:

empirical standard deviation of test statistic for random shuffles

perm.gamma:

in case rococo.test was called with storeValues=TRUE, this slot contains the vector of test statistics for random shuffles.

alternative:

alternative hypothesis used by rococo.test.

Methods

show

signature(object = "RococoTestResults"): d displays the most important information stored in object

Author(s)

Martin Krone and Ulrich Bodenhofer

References

https://github.com/UBod/rococo

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.

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.

See Also

rococo.test, rococo, show-methods

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)

## perform correlation tests
ret <- rococo.test(x, y, similarity="classical", alternative="greater")
show(ret)

ret <- rococo.test(x, y, similarity="linear", alternative="greater")
show(ret)

ret <- rococo.test(x, y, similarity=c("classical", "gauss"),
                   r=c(0, 0.1), alternative="greater",
                   numtests=10000)
show(ret)

---