Builds a Rank Correlation using the Iman and Connover Method.
This function builds a rank correlation structure between columns of a matrix or between mcnode objects using the Iman and Connover method (1982).
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).
A scalar (only if n=2) or a (n x n) matrix of correlation.
Should the order be returned?
Should the correlation eventually obtained be printed?
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
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.
Connover W., Iman R. (1982). A distribution-free approach to inducing rank correlation among input variables. Technometric, 3, 311-334.
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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")
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