This function attempts to correct the final pairwise correlations of simulated variables to be within epsilon
of the target correlations. It updates the intermediate normal correlation iteratively in a loop until either the maximum error
is less than epsilon or the number of iterations exceeds maxit. This function would not ordinarily be called directly by
the user. The function is a modification of Barbiero & Ferrari's ordcont function in
GenOrd-package. The ordcont function has been modified in the following ways:
1) It works for continuous, ordinal (r >= 2 categories), and count (regular or zero-inflated, Poisson or Negative Binomial) variables.
2) The initial correlation check has been removed because the intermediate correlation matrix
Sigma from corrvar or corrvar2 has already been
checked for positive-definiteness and used to generate variables.
3) Eigenvalue decomposition is done on Sigma to impose the correct intermediate correlations on the normal variables.
If Sigma is not positive-definite, the negative eigenvalues are replaced with 0.
4) The final positive-definite check has been removed.
5) The intermediate correlation update function was changed to accommodate more situations.
6) Allowing specifications for the sample size and the seed for reproducibility.
The vignette Variable Types describes the algorithm used in the error loop.
corr_error(n = 10000, k_cat = 0, k_cont = 0, k_pois = 0, k_nb = 0,
method = c("Fleishman", "Polynomial"), means = NULL, vars = NULL,
constants = NULL, marginal = list(), support = list(), lam = NULL,
p_zip = 0, size = NULL, mu = NULL, p_zinb = 0, seed = 1234,
epsilon = 0.001, maxit = 1000, rho0 = NULL, Sigma = NULL,
rho_calc = NULL)the sample size
the number of ordinal (r >= 2 categories) variables
the number of continuous variables (these may be regular continuous variables or components of continuous mixture variables)
the number of Poisson (regular or zero-inflated) variables
the number of Negative Binomial (regular or zero-inflated) variables
the method used to generate the continuous variables. "Fleishman" uses a third-order polynomial transformation and "Polynomial" uses Headrick's fifth-order transformation.
a vector of means for the continuous variables
a vector of variances for the continuous variables
a matrix with k_cont rows, each a vector of constants c0, c1, c2, c3 (if method = "Fleishman") or
c0, c1, c2, c3, c4, c5 (if method = "Polynomial"), like that returned by find_constants
a list of length equal k_cat; 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)
a list of length equal k_cat; the i-th element is a vector of containing the r
ordered support values; if not provided, the default is for the i-th element to be the vector 1, ..., r
a vector of lambda (mean > 0) constants for the Poisson variables (see stats::dpois); the order should be
1st regular Poisson variables, 2nd zero-inflated Poisson variables
a vector of probabilities of structural zeros (not including zeros from the Poisson distribution) for the zero-inflated
Poisson variables (see VGAM::dzipois)
a vector of size parameters for the Negative Binomial variables (see stats::dnbinom); the order should be
1st regular NB variables, 2nd zero-inflated NB variables
a vector of mean parameters for the NB variables; order the same as in size; for zero-inflated NB this refers to
the mean of the NB distribution (see VGAM::dzinegbin)
a vector of probabilities of structural zeros (not including zeros from the NB distribution) for the zero-inflated NB variables
(see VGAM::dzinegbin)
the seed value for random number generation
the maximum acceptable error between the final and target pairwise correlation; smaller epsilons take more time
the maximum number of iterations to use to find the intermediate correlation; the
correction loop stops when either the iteration number passes maxit or epsilon is reached
the target correlation matrix
the final correlation matrix calculated in corrvar
or corrvar2 before execution of corr_error
A list with the following components:
Sigma the intermediate MVN correlation matrix resulting from the error loop
rho_calc the calculated final correlation matrix generated from Sigma
Y_cat the ordinal variables
Y the continuous (mean 0, variance 1) variables
Y_cont the continuous variables with desired mean and variance
Y_pois the Poisson variables
Y_nb the Negative Binomial variables
niter a matrix containing the number of iterations required for each variable pair
Please see references for SimCorrMix.