This function calculates the maximum support value for count variables by extending the method of Barbiero &
Ferrari (2015, 10.1002/asmb.2072) to include regular and zero-inflated Poisson and Negative Binomial variables. In order for
count variables to be treated as ordinal in the calculation of the intermediate MVN correlation matrix, their infinite support must
be truncated (made finite). This is done by setting the total cumulative probability equal to 1 - a small user-specified value
(pois_eps
or nb_eps
). The maximum support value equals the inverse CDF applied to this result. The truncation values
may differ for each variable. The function is used in intercorr2
and corrvar2
and
would not ordinarily be called by the user.
maxcount_support(k_pois = 0, k_nb = 0, lam = NULL, p_zip = 0,
size = NULL, prob = NULL, mu = NULL, p_zinb = 0, pois_eps = NULL,
nb_eps = NULL)
the number of Poisson variables
the number of Negative Binomial variables
a vector of lambda (mean > 0) constants for the regular and zero-inflated Poisson variables (see stats::dpois
);
the order should be 1st regular Poisson variables, 2nd zero-inflated Poisson variables
a vector of probabilities of structural zeros (not including zeros from the Poisson distribution) for the
zero-inflated Poisson variables (see VGAM::dzipois
); if p_zip
= 0, \(Y_{pois}\) has a regular Poisson
distribution; if p_zip
is in (0, 1), \(Y_{pois}\) has a zero-inflated Poisson distribution;
if p_zip
is in (-(exp(lam) - 1)^(-1), 0)
, \(Y_{pois}\) has a zero-deflated Poisson distribution and p_zip
is not a probability; if p_zip = -(exp(lam) - 1)^(-1)
, \(Y_{pois}\) has a positive-Poisson distribution
(see VGAM::dpospois
); if length(p_zip) < length(lam)
, the missing values are set to 0 (and ordered 1st)
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 success probability parameters for the NB variables; order the same as in size
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)
a vector of length k_pois
containing total cumulative probability truncation values; if none are provided,
the default is 0.0001 for each variable
a vector of length k_nb
containing total cumulative probability truncation values; if none are provided,
the default is 0.0001 for each variable
a data.frame with k_pois + k_nb
rows; the column names are:
Distribution
Poisson or Negative Binomial
Number
the variable index
Max
the maximum support value
Barbiero A & Ferrari PA (2015). Simulation of correlated Poisson variables. Applied Stochastic Models in Business and Industry, 31:669-80. 10.1002/asmb.2072.