Find initial correlation matrix for NORTA from target correlation

This function can be used to find a suitable correlation matrix to be used for simulating initial multivariate normal data in a NORTA based simulation design (see simdesign_norta).

Usage

optimize_cor_mat(
  cor_target,
  dist,
  ensure_cor_mat = TRUE,
  conv_norm_type = "O",
  return_diagnostics = FALSE,
  ...
)

Arguments

cor_target

Target correlation matrix.

dist

List of functions of marginal distributions for simulated variables. Must have the same length as the specified correlation matrix (cor_target), and the order of the entries must correspond to the variables in the correlation matrix. See simdesign_norta for details of the specification of the marginal distributions.

ensure_cor_mat

if TRUE, this function ensures that the optimized matrix is a proper correlation matrix by ensuring positive definitiness. If FALSE, the optimized matrix is returned as is.

conv_norm_type

Metric to be used to find closest positive definite matrix to optimal matrix, used if ensure_cor_mat is TRUE. Passed to Matrix::nearPD.

return_diagnostics

TRUE to return additional diagnostics of the optimization procedure, see below.

...

Additional parameters passed to optimize_cor_for_pair.

Value

If return_diagnostics is FALSE, a correlation matrix to be used in the definition of a simdesign_norta object. If TRUE, then a list with two entries: cor_mat containing the correlation matrix, and convergence containing a list of objects returned by the individual optimisation problems from stats::uniroot.

Details

This function first finds a suitable correlation matrix for the underlying multivariate normal data used in the NORTA procedure. It does so by solving k*(k-1) univariable optimisation problems (where k is the number of variables). In case the result is not a positive-definite matrix, the nearest positive-definite matrix is found according to the user specified metric using Matrix::nearPD. See e.g. Ghosh and Henderson (2003) for an overview of the procedure.

References

Ghosh, S. and Henderson, S. G. (2003) Behavior of the NORTA method for correlated random vector generation as the dimension increases. ACM Transactions on Modeling and Computer Simulation.

See also

simdesign_norta