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, 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,
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.
intercorr_cont_nb(method = c("Fleishman", "Polynomial"), constants = NULL,
rho_cont_nb = NULL, size = NULL, mu = NULL, p_zinb = 0,
nrand = 100000, seed = 1234)
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.
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 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
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 (*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
)
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)
the number of random numbers to generate in calculating the bound (default = 10000)
the seed used in random number generation (default = 1234)
a k_cont x k_nb
matrix whose rows represent the k_cont
continuous variables and columns represent the
k_nb
Negative Binomial variables
Please see references for intercorr_cont_pois
.