findintercorr_nb: Calculate Intermediate MVN Correlation for Negative Binomial...
In SimMultiCorrData: Simulation of Correlated Data with Multiple Variable Types

Description Usage Arguments Value References See Also

This function calculates a k_nb x k_nb intermediate matrix of correlations for the Negative Binomial variables by extending the method of Yahav & Shmueli (2012, doi: 10.1002/asmb.901). The intermediate correlation between Z1 and Z2 (the standard normal variables used to generate the Negative Binomial variables Y1 and Y2 via the inverse cdf method) is calculated using a logarithmic transformation of the target correlation. First, the upper and lower Frechet-Hoeffding bounds (mincor, maxcor) on ρ_{y1,y2} are simulated. Then the intermediate correlation is found as follows:

ρ_{z1,z2} = (1/b) * log((ρ_{y1,y2} - c)/a)

, where a = -(maxcor * mincor)/(maxcor + mincor), b = log((maxcor + a)/a), and c = -a. The function adapts code from Amatya & Demirtas' (2016) package PoisNor-package by:

1) allowing specifications for the number of random variates and the seed for reproducibility

2) providing the following checks: if ρ_{z1,z2} >= 1, ρ_{z1,z2} is set to 0.99; if ρ_{z1,z2} <= -1, ρ_{z1,z2} is set to -0.99

3) simulating Negative Binomial variables.

The function is used in findintercorr and rcorrvar. This function would not ordinarily be called by the user.

1 2	findintercorr_nb(rho_nb, size, prob, mu = NULL, nrand = 100000, seed = 1234)

`rho_nb`	a `k_nb x k_nb` matrix of target correlations
`size`	a vector of size parameters for the Negative Binomial variables (see `NegBinomial`)
`prob`	a vector of success probability parameters
`mu`	a vector of mean parameters (*Note: either `prob` or `mu` should be supplied for all Negative Binomial variables, not a mixture; default = NULL)
`nrand`	the number of random numbers to generate in calculating the bound (default = 10000)
`seed`	the seed used in random number generation (default = 1234)