GenOrd (version 1.3.0)

ordcont: Computing the "intermediate" correlation matrix for the multivariate standard normal in order to achieve the "target" correlation matrix for the ordinal/discrete variables

Description

The function computes the correlation matrix of the $k$-dimensional standard normal r.v. yielding the desired correlation matrix Sigma for the $k$-dimensional r.v. with desired marginal distributions marginal

Usage

ordcont(marginal,Sigma,support=list(),Spearman=FALSE,epsilon=1e-06,maxit=100)

Arguments

marginal

a list of $k$ elements, where $k$ is the number of variables. The $i$-th element of marginal is the vector of the cumulative probabilities defining the marginal distribution of the $i$-th component of the multivariate variable. If the $i$-t

Sigma

the target correlation matrix of the ordinal/discrete variables

support

a list of $k$ elements, where $k$ is the number of variables. The $i$-th element of support contains the ordered values of the support of the $i$-th variable. By default, the support of the $i$-th variable is $1,2,...,k_i$

Spearman

if TRUE, the function finds Spearman's correlations (and it is not necessary to provide support), if FALSE (default) Pearson's correlations

epsilon

the maximum tolerated error among target and actual correlations

maxit

the maximum number of iterations allowed for the algorithm

Value

• a list of five elements
• SigmaC
  the correlation matrix of the multivariate standard normal variable
• SigmaO
  the actual correlation matrix of the discretized variables (it should approximately coincide with the target correlation matrix Sigma)
• Sigma
  the target correlation matrix of the ordinal/discrete variables
• niter
  a matrix containing the number of iterations performed by the algorithm, one for each pair of variables
• maxerr
  the actual maximum error (the absolute maximum deviation between actual and target correlations of the ordinal/discrete variables)

See Also

contord, ordsample, corrcheck

Examples

# consider a 4-dimensional ordinal variable
k <- 4
# with different number of categories
kj <- c(2,3,4,5)
# and uniform marginal distributions
marginal <- list(0.5,c(1/3,2/3), c(1/4,2/4,3/4), c(1/5,2/5,3/5,4/5))
corrcheck(marginal)
# and the following correlation matrix
Sigma <- matrix(c(1,0.5,0.4,0.3,0.5,1,0.5,0.4,0.4,0.5,1,0.5,0.3,0.4,0.5,1),4,4,byrow=TRUE)
Sigma
# the correlation matrix of the standard 4-dimensional standard normal
# ensuring Sigma is
res <- ordcont(marginal, Sigma)
res[[1]]
# change some marginal distributions
marginal <- list(0.3, c(1/3,2/3), c(1/5,2/5,3/5), c(0.1,0.2,0.4,0.6))
corrcheck(marginal)
# and notice how the correlation matrix of the multivariate normal changes...
res <- ordcont(marginal, Sigma)
res[[1]]
# change Sigma, adding a negative correlation
Sigma[1,2] <- -0.2
Sigma[2,1] <- Sigma[1,2]
Sigma
# checking whether Sigma is still positive definite
eigen(Sigma)$values # all >0, OK
res <- ordcont(marginal, Sigma)
res[[1]]