cornode: Builds a Rank Correlation using the Iman and Conover Method.
In mc2d: Tools for Two-Dimensional Monte-Carlo Simulations

Description Usage Arguments Details Value References Examples

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

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

`...`	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.

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 colums (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).

If rank = FALSE: the matrix or a list of rearranged mcnodes.

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

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.

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")

Loading required package: mvtnorm

Attaching package: 'mc2d'

The following objects are masked from 'package:base':

    pmax, pmin

     [,1] [,2] [,3]
[1,]  1.0  0.5  0.2
[2,]  0.5  1.0  0.2
[3,]  0.2  0.2  1.0
             x1          x2           x3
x1  1.000000000 -0.09934766 -0.007409839
x2 -0.099347655  1.00000000  0.013825010
x3 -0.007409839  0.01382501  1.000000000
Spearman Rank Correlation Post Function
          x1        x2        x3
x1 1.0000000 0.4998972 0.1956993
x2 0.4998972 1.0000000 0.1659506
x3 0.1956993 0.1659506 1.0000000
[1] TRUE
                  cook    roundserv      serving
cook       1.000000000 -0.006836998 -0.006485743
roundserv -0.006836998  1.000000000  0.999873506
serving   -0.006485743  0.999873506  1.000000000
                cook        serv      serving
cook     1.000000000  0.41659472 -0.006485743
serv     0.416594717  1.00000000 -0.037856354
serving -0.006485743 -0.03785635  1.000000000
               cook roundserv   serving
cook      1.0000000 0.4322883 0.4330319
roundserv 0.4322883 1.0000000 0.9998735
serving   0.4330319 0.9998735 1.0000000