I am trying to use R to simulate random variations in a real dataset with a known number of categorical and continuous predictor variables, as well as known marginal probabilities for each ordinal/categorical variable. These parameters are as follows:

ncont <- 4  # number of continuous predictor variables
ncat  <- 8  # number of categorical predictor variables

margprobs <- list(c(0.24, 0.3, 0.28),
                  c(0.01, 0.071, 0.17, 0.069, 0.005, 0.05),
                  c(0.07, 0.06, 0.14, 0.3),
                  c(0.05, 0.45, 0.5),
                  c(0.05, 0.8),

I can simulate this dataset if I assume that the categorical variables are independent, and I can create valid correlation matrices for just the continuous variables. However, every time I try to create a simulated variance-covariance or correlation matrix for the categorical variables, it is not valid in the context of the known marginal probabilities.

I have consulted the vignettes for the OrdNor, SimCorrMix, and SimMultiCorrData packages for how to produce a valid correlation or variance-covariance matrix with known marginal probabilities, but I can't figure it out. I can use these packages to find the upper and lower bounds of acceptable correlations in the context of the marginal probabilities, but every correlation matrix I sample passes the validation check these packages provide but ultimately fails when being converted to an intermediate correlation matrix. I provide some example code for this below:

margprobs <- lapply(margprobs, FUN=sort)  # must sort margprobs for corrvar() to work
corlims   <- validcorr(1000, k_cat=8, marginal=margprobs)

Rey <- diag(8)
for (i in 1:nrow(Rey)) {
  for (j in 1:ncol(Rey)) {
    if (i > j) Rey[i, j] <- runif(1, corlims$L_rho[i, j], corlims$U_rho[i, j])
    Rey[j, i] <- Rey[i, j]

# Check to see if Rey is positive-definite
min(eigen(Rey, symmetric=TRUE)$values) < 0

# Use SimCorrMix to check for valid correlation matrix
validcorr(1000, k_cat=8, marginal=margprobs, rho=Rey)

ords1 <- corrvar(1000, k_cat=8, marginal=margprobs, rho=Rey)
# Error message: It is not possible to find a correlation matrix for MVN 
# ensuring rho for the ordinal variables.  Try the error loop.
# Intermediate correlation matrix is not positive definite. Nearest 
# positive definite matrix is used.

# Note: this error happens whether or not I use Matrix::nearPD or 
# psych::cor.smooth to ensure that the rho matrix is positive definite

Please help me understand how to create a valid ordinal correlation matrix that will work with these simulations.

I want to eventually produce a simulation of continuous and categorical variables based on a valid correlation matrix for all variables, and then I can see how the magnitudes of these correlations affect the ability of models to recover known coefficients (beta) and outcome values (y) that I provide in the simulations.


According to the manual page of corrvar, "marginal" should be a vector of cumulative probabilities excluding the last (which is always = 1). So instead of c(0.24, 0.3, 0.28), for example, try cumsum(c(0.24, 0.3, 0.28)).


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