intercorr_nb {SimCorrMix}

Calculate Intermediate MVN Correlation for Negative Binomial Variables: Correlation Method 1

Description

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 \rho_{Y1, Y2} are simulated. Then the intermediate correlation is found as follows:

\rho_{Z1, Z2} = \frac{1}{b} * log(\frac{\rho_{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 Sigma_(Z1, Z2) > 1, Sigma_(Z1, Z2) is set to 1; if Sigma_(Z1, Z2) < -1, Sigma_(Z1, Z2) is set to -1

3) simulating regular and zero-inflated Negative Binomial variables.

The function is used in intercorr and corrvar and would not ordinarily be called by the user.

Usage

intercorr_nb(rho_nb = NULL, size = NULL, mu = NULL, p_zinb = 0,
  nrand = 100000, seed = 1234)

Arguments

rho_nb

a k_nb x k_nb matrix of target correlations ordered 1st regular and 2nd zero-inflated

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 (*Note: either prob or mu should be supplied for all Negative Binomial variables, not a mixture; default = NULL); 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); if p_zinb = 0, Y_{nb} has a regular NB distribution; if p_zinb is in (-prob^size/(1 - prob^size), 0), Y_{nb} has a zero-deflated NB distribution and p_zinb is not a probability; if p_zinb = -prob^size/(1 - prob^size), Y_{nb} has a positive-NB distribution (see VGAM::dposnegbin); if length(p_zinb) < length(size), the missing values are set to 0 (and ordered 1st)

nrand

the number of random numbers to generate in calculating the bound (default = 10000)

seed

the seed used in random number generation (default = 1234)

Value

the k_nb x k_nb intermediate correlation matrix for the Negative Binomial variables

References

Please see references for intercorr_pois.

See Also

intercorr_pois, intercorr_pois_nb, intercorr, corrvar