contord {GenOrd}

Correlations of discretized variables

Description

The function computes the correlation matrix of the k variables, with given marginal distributions, derived discretizing a k-variate standard normal variable with given correlation matrix

Usage

contord(marginal, Sigma, support = list(), Spearman = FALSE)

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-th component can take k_i values, the i-th element of marginal will contain k_i-1 probabilities (the k_i-th is obviously 1 and shall not be included).

Sigma

the correlation matrix of the standard multivariate normal variable

support

a list of k elements, where k is the number of variables. The i-th element of support is the vector containing 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

Value

the correlation matrix of the discretized variables

Author(s)

Alessandro Barbiero, Pier Alda Ferrari

See Also

ordcont, ordsample, corrcheck

Examples

# consider 4 discrete variables
k <- 4
# with these marginal distributions
marginal <- list(0.4,c(0.3,0.6), c(0.25,0.5,0.75), c(0.1,0.2,0.8,0.9))
# generated discretizing a multivariate standard normal variable
# with correlation matrix
Sigma <- matrix(0.5,4,4)
diag(Sigma) <- 1
# the resulting correlation matrix for the discrete variables is
contord(marginal, Sigma)
# note all the correlations are smaller than the original 0.6
# change Sigma, adding a negative correlation
Sigma[1,2] <- -0.15
Sigma[2,1] <- Sigma[1,2]
Sigma
# checking whether Sigma is still positive definite
eigen(Sigma)$values # all >0, OK
contord(marginal, Sigma)