This function calculates the correlation of ordinal variables (or variables treated as "ordinal"), with given marginal
distributions, obtained from discretizing standard normal variables with a specified correlation matrix. The function modifies
Barbiero & Ferrari's contord
function in GenOrd-package
. It uses
pmvnorm
function from the mvtnorm package to calculate multivariate normal cumulative probabilities
defined by the normal quantiles obtained at marginal
and the supplied correlation matrix Sigma
. This function is used
within ord_norm
and would not ordinarily be called by the user.
norm_ord(marginal = list(), Sigma = NULL, support = list(),
Spearman = FALSE)
a list of length equal to the number of variables; the i-th element is a vector of the cumulative probabilities defining the marginal distribution of the i-th variable; if the variable can take r values, the vector will contain r - 1 probabilities (the r-th is assumed to be 1)
the correlation matrix of the multivariate standard normal variable
a list of length equal to the number of variables; the i-th element is a vector of containing the r ordered support values; if not provided (i.e. support = list()), the default is for the i-th element to be the vector 1, ..., r
if TRUE, Spearman's correlations are used (and support is not required); if FALSE (default) Pearson's correlations are used
the correlation matrix of the ordinal variables
Please see references in ord_norm
.
Alan Genz, Frank Bretz, Tetsuhisa Miwa, Xuefei Mi, Friedrich Leisch, Fabian Scheipl, Torsten Hothorn (2018). mvtnorm: Multivariate Normal and t Distributions. R package version 1.0-8. https://CRAN.R-project.org/package=mvtnorm.
Alan Genz, Frank Bretz (2009), Computation of Multivariate Normal and t Probabilities. Lecture Notes in Statistics, Vol. 195., Springer-Verlag, Heidelberg. ISBN 978-3-642-01688-2.