# Builds a Rank Correlation using the Iman and Conover Method. This function builds a rank correlation structure between columns of a matrix or between mcnode objects using the Iman and Conover method (1982). ```r cornode(..., target, outrank=FALSE, result=FALSE, seed=NULL) ``` ## Examples ```r 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") ``` ## 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). ## Returns 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.

cornode function