intercorr_cont_nb: Calculate Intermediate MVN Correlation for Continuous -... In SimCorrMix: Simulation of Correlated Data with Multiple Variable Types Including Continuous and Count Mixture Distributions

Description

This function calculates a `k_cont x k_nb` intermediate matrix of correlations for the `k_cont` continuous and `k_nb` Negative Binomial variables. It extends the method of Amatya & Demirtas (2015, doi: 10.1080/00949655.2014.953534) to continuous variables generated using Headrick's fifth-order polynomial transformation and regular or zero-inflated NB variables. Here, the intermediate correlation between Z1 and Z2 (where Z1 is the standard normal variable transformed using Headrick's fifth-order or Fleishman's third-order method to produce a continuous variable Y1, and Z2 is the standard normal variable used to generate a Negative Binomial variable via the inverse CDF method) is calculated by dividing the target correlation by a correction factor. The correction factor is the product of the upper Frechet-Hoeffding bound on the correlation between a Negative Binomial variable and the normal variable used to generate it and the power method correlation (described in Headrick & Kowalchuk, 2007, doi: 10.1080/10629360600605065) between Y1 and Z1. The function is used in `intercorr` and `corrvar`. This function would not ordinarily be called by the user.

Usage

 ```1 2 3``` ```intercorr_cont_nb(method = c("Fleishman", "Polynomial"), constants = NULL, rho_cont_nb = NULL, size = NULL, mu = NULL, p_zinb = 0, nrand = 100000, seed = 1234) ```

Arguments

 `method` the method used to generate the `k_cont` continuous variables. "Fleishman" uses a third-order polynomial transformation and "Polynomial" uses Headrick's fifth-order transformation. `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` `rho_cont_nb` a `k_cont x k_nb` matrix of target correlations among continuous and Negative Binomial variables; the NB variables should be ordered 1st regular, 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

a `k_cont x k_nb` matrix whose rows represent the `k_cont` continuous variables and columns represent the `k_nb` Negative Binomial variables

References

Please see references for `intercorr_cont_pois`.

`find_constants`, `intercorr`, `corrvar`