corr_error {SimCorrMix}

Error Loop to Correct Final Correlation of Simulated Variables

Description

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.

Usage

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)

Arguments

n

the sample size

k_cat

the number of ordinal (r >= 2 categories) variables

k_cont

the number of continuous variables (these may be regular continuous variables or components of continuous mixture variables)

k_pois

the number of Poisson (regular or zero-inflated) variables

k_nb

the number of Negative Binomial (regular or zero-inflated) variables

method

the method used to generate the continuous variables. "Fleishman" uses a third-order polynomial transformation and "Polynomial" uses Headrick's fifth-order transformation.

means

a vector of means for the continuous variables

vars

a vector of variances for the continuous variables

constants

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

marginal

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)

support

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

lam

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

p_zip

a vector of probabilities of structural zeros (not including zeros from the Poisson distribution) for the zero-inflated Poisson variables (see VGAM::dzipois)

size

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

mu

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)

p_zinb

a vector of probabilities of structural zeros (not including zeros from the NB distribution) for the zero-inflated NB variables (see VGAM::dzinegbin)

seed

the seed value for random number generation

epsilon

the maximum acceptable error between the final and target pairwise correlation; smaller epsilons take more time

maxit

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

rho0

the target correlation matrix

Sigma

the intermediate correlation matrix previously used in corrvar or corrvar2

rho_calc

the final correlation matrix calculated in corrvar or corrvar2 before execution of corr_error

Value

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

References

Please see references for SimCorrMix.

See Also

corrvar, corrvar2