This function calculates the k_cat x k_nb
intermediate matrix of correlations for the k_cat
ordinal (\(r >=
2\) categories) and k_nb
Negative Binomial variables required to produce the target correlations in rho_cat_nb
. It extends the method of Amatya & Demirtas (2015, 10.1080/00949655.2014.953534)
to ordinal - Negative Binomial pairs and allows for regular or zero-inflated NB variables. Here, the intermediate correlation between Z1 and Z2 (where Z1 is the standard normal variable
discretized to produce an ordinal 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 a simulated GSC upper bound on the correlation between an ordinal variable and the normal variable used to generate it (see Demirtas & Hedeker, 2011,
10.1198/tast.2011.10090). The function is used in intercorr
and corrvar
.
This function would not ordinarily be called by the user.
intercorr_cat_nb(rho_cat_nb = NULL, marginal = list(), size = NULL,
mu = NULL, p_zinb = 0, nrand = 100000, seed = 1234)
a k_cat x k_nb
matrix of target correlations among ordinal and Negative Binomial variables; the NB variables
should be ordered 1st regular, 2nd zero-inflated
a list of length equal to 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)
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_cat x k_nb
matrix whose rows represent the k_cat
ordinal variables and columns represent the
k_nb
Negative Binomial variables
Please see references for intercorr_cat_pois
.