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
contord(marginal, Sigma, support = list(), Spearman = FALSE)
a list of $k$ elements, where $k$ is the number of variables.
The $i$-th element of
marginalis 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
marginalwill contain $k_i-1$ probabilities (the $k_i$-th is obviously 1 and shall not be included).
- the correlation matrix of the standard multivariate normal variable
a list of $k$ elements, where $k$ is the number of variables. The $i$-th element of
supportis the vector containing the ordered values of the support of the $i$-th variable. By default, the support of the $i$-th variable is $1,2,...,k_i$
TRUE, the function finds Spearman's correlations (and it is not necessary to provide
FALSE(default) Pearson's correlations
the correlation matrix of the discretized variables
# 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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