contord
From GenOrd v1.4.0
by Alessandro Barbiero
Correlations of discretized variables
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
 Keywords
 multivariate, models, distribution, htest, datagen
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 ofmarginal
will contain $k_i1$ 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 providesupport
), ifFALSE
(default) Pearson's correlations
Value

the correlation matrix of the discretized variables
See Also
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)
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