cornode: Builds a Rank Correlation using the Iman and Conover Method.

In mc2d: Tools for Two-Dimensional Monte-Carlo Simulations

Builds a Rank Correlation using the Iman and Conover Method.

Description

This function builds a rank correlation structure between columns of a matrix or between ‘⁠mcnode⁠’ objects using the Iman and Conover method (1982).

Usage

cornode(..., target, outrank=FALSE, result=FALSE, seed=NULL)

Arguments

...	A matrix (each of its ‘⁠n⁠’ columns but the first one will be reordered) or ‘⁠n mcnode⁠’ objects (each elements but the first one will be reordered).
target	A scalar (only if ‘⁠n=2⁠’) or a ‘⁠(n x n)⁠’ matrix of correlation.
outrank	Should the order be returned?
result	Should the correlation eventually obtained be printed?
seed	The random seed used for building the correlation. If ‘⁠NULL⁠’ the ‘⁠seed⁠’ is unchanged.

Details

The arguments should be named.

The function accepts for ‘⁠data⁠’ a matrix or:

• some ‘⁠"V" mcnode⁠’ objects separated by a comma;

• some ‘⁠"U" mcnode⁠’ objects separated by a comma;

• some ‘⁠"VU" mcnode⁠’ objects separated by a comma. In that case, the structure is built columns by columns (the first column of each ‘⁠"VU" mcnode⁠’ will have a correlation structure, the second ones will have a correlation structure, ....).

• one ‘⁠"V" mcnode⁠’ as a first element and some ‘⁠"VU" mcnode⁠’ objects, separated by a comma. In that case, the structure is built between the ‘⁠"V" mcnode⁠’ and each column of the ‘⁠"VU" mcnode⁠’ objects. The correlation result (‘⁠result = TRUE⁠’) is not provided in that case.

The number of variates of the elements should be equal.

‘⁠target⁠’ should be a scalar (two columns only) or a real symmetric positive-definite square matrix. Only the upper triangular part of ‘⁠target⁠’ is used (see chol).

The final correlation structure should be checked because it is not always possible to build the target correlation structure.

In a Monte-Carlo simulation, note that the order of the values within each ‘⁠mcnode⁠’ will be changed by this function (excepted for the first one of the list). As a consequence, previous links between variables will be broken. The ‘⁠outrank⁠’ option may help to rebuild these links (see the Examples).

Value

If ‘⁠rank = FALSE⁠’: the matrix or a list of rearranged ‘⁠mcnode⁠’s.

If ‘⁠rank = TRUE⁠’: the order to be used to rearranged the matrix or the ‘⁠mcnodes⁠’ to build the desired correlation structure.

References

Iman, R. L., & Conover, W. J. (1982). A distribution-free approach to inducing rank correlation among input variables. Communication in Statistics - Simulation and Computation, 11(3), 311-334.

Examples

x1 <- rnorm(1000)
x2 <- rnorm(1000)
x3 <- rnorm(1000)
mat <- cbind(x1, x2, x3)
## Target
(corr <- matrix(c(1, 0.5, 0.2, 0.5, 1, 0.2, 0.2, 0.2, 1), ncol=3))
## Before
cor(mat, method="spearman")
matc <- cornode(mat, target=corr, result=TRUE)
## The first row is unchanged
all(matc[, 1] == mat[, 1])

##Using mcnode and outrank
cook <- mcstoc(rempiricalD, values=c(0, 1/5, 1/50), prob=c(0.027, 0.373, 0.600), nsv=1000)
serving <- mcstoc(rgamma, shape=3.93, rate=0.0806, nsv=1000)
roundserv <- mcdata(round(serving), nsv=1000)
## Strong relation between roundserv and serving (of course)
cor(cbind(cook, roundserv, serving), method="spearman")

##The classical way to build the correlation structure 
matcorr <- matrix(c(1, 0.5, 0.5, 1), ncol=2)
matc <- cornode(cook=cook, roundserv=roundserv, target=matcorr)
## The structure between cook and roundserv is OK but ...
## the structure between roundserv and serving is lost
cor(cbind(cook=matc$cook, serv=matc$roundserv, serving), method="spearman")

##An alternative way to build the correlation structure
matc <- cornode(cook=cook, roundserv=roundserv, target=matcorr, outrank=TRUE)
## Rebuilding the structure
roundserv[] <- roundserv[matc$roundserv, , ]
serving[] <- serving[matc$roundserv, , ]
## The structure between cook and roundserv is OK and ...
## the structure between roundserv and serving is preserved
cor(cbind(cook, roundserv, serving), method="spearman")

mc2d documentation built on July 26, 2023, 6:07 p.m.