maxcount_support

k_pois

the number of Negative Binomial variables

k_nb

a vector of lambda (mean &gt; 0) constants for the regular and zero-inflated Poisson variables (see <code>stats::dpois</code>);
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 <code>VGAM::dzipois</code>); if <code>p_zip</code> = 0, \(Y_{pois}\) has a regular Poisson
distribution; if <code>p_zip</code> is in (0, 1), \(Y_{pois}\) has a zero-inflated Poisson distribution;
if <code>p_zip</code> is in <code>(-(exp(lam) - 1)^(-1), 0)</code>, \(Y_{pois}\) has a zero-deflated Poisson distribution and <code>p_zip</code>
is not a probability; if <code>p_zip = -(exp(lam) - 1)^(-1)</code>, \(Y_{pois}\) has a positive-Poisson distribution
(see <code>VGAM::dpospois</code>); if <code>length(p_zip) &lt; length(lam)</code>, the missing values are set to 0 (and ordered 1st)

p_zip

a vector of size parameters for the Negative Binomial variables (see <code>stats::dnbinom</code>); the order should be
1st regular NB variables, 2nd zero-inflated NB variables

size

a vector of success probability parameters for the NB variables; order the same as in <code>size</code>

prob

a vector of mean parameters for the NB variables (*Note: either <code>prob</code> or <code>mu</code> should be supplied for all Negative Binomial variables,
not a mixture; default = NULL); order the same as in <code>size</code>; for zero-inflated NB this refers to
the mean of the NB distribution (see <code>VGAM::dzinegbin</code>)

a vector of probabilities of structural zeros (not including zeros from the NB distribution) for the zero-inflated NB variables
(see <code>VGAM::dzinegbin</code>); if <code>p_zinb</code> = 0, \(Y_{nb}\) has a regular NB distribution;
if <code>p_zinb</code> is in <code>(-prob^size/(1 - prob^size),</code> <code>0)</code>, \(Y_{nb}\) has a zero-deflated NB distribution and <code>p_zinb</code>
is not a probability; if <code>p_zinb = -prob^size/(1 - prob^size)</code>, \(Y_{nb}\) has a positive-NB distribution (see
<code>VGAM::dposnegbin</code>); if <code>length(p_zinb) &lt; length(size)</code>, the missing values are set to 0 (and ordered 1st)

p_zinb

a vector of length <code>k_pois</code> containing total cumulative probability truncation values; if none are provided,
the default is 0.0001 for each variable

pois_eps

a vector of length <code>k_nb</code> containing total cumulative probability truncation values; if none are provided,
the default is 0.0001 for each variable

nb_eps

This function calculates the maximum support value for count variables by extending the method of Barbiero &amp;
 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
 (<code>pois_eps</code> or <code>nb_eps</code>). 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 <code><a rd-options="SimCorrMix" href="/link/intercorr2?package=SimCorrMix&version=0.1.1&to=SimCorrMix" data-mini-rdoc="SimCorrMix::intercorr2">intercorr2</a></code> and <code><a rd-options="SimCorrMix" href="/link/corrvar2?package=SimCorrMix&version=0.1.1&to=SimCorrMix" data-mini-rdoc="SimCorrMix::corrvar2">corrvar2</a></code> and
 would not ordinarily be called by the user.

poisson

NegativeBinomial

method2

Generate continuous (normal, non-normal, or mixture distributions), binary, ordinal,
and count (regular or zero-inflated, Poisson or Negative Binomial) variables with a specified
correlation matrix, or one continuous variable with a mixture distribution. This package can
be used to simulate data sets that mimic real-world clinical or genetic data sets (i.e.,
plasmodes, as in Vaughan et al., 2009 <DOI:10.1016/j.csda.2008.02.032>). The methods
extend those found in the 'SimMultiCorrData' R package. Standard normal variables with an
imposed intermediate correlation matrix are transformed to generate the desired distributions.
Continuous variables are simulated using either Fleishman (1978)'s third order
<DOI:10.1007/BF02293811> or Headrick (2002)'s fifth order
<DOI:10.1016/S0167-9473(02)00072-5> polynomial transformation method (the power method
transformation, PMT). Non-mixture distributions require the user to specify mean, variance,
skewness, standardized kurtosis, and standardized fifth and sixth cumulants. Mixture
distributions require these inputs for the component distributions plus the mixing
probabilities. Simulation occurs at the component level for continuous mixture
distributions. The target correlation matrix is specified in terms of correlations with
components of continuous mixture variables. These components are transformed into the
desired mixture variables using random multinomial variables based on the mixing
probabilities. However, the package provides functions to approximate expected correlations
with continuous mixture variables given target correlations with the components. Binary and
ordinal variables are simulated using a modification of ordsample() in package 'GenOrd'.
Count variables are simulated using the inverse CDF method. There are two simulation
pathways which calculate intermediate correlations involving count variables differently.
Correlation Method 1 adapts Yahav and Shmueli's 2012 method <DOI:10.1002/asmb.901> and
performs best with large count variable means and positive correlations or small means and
negative correlations. Correlation Method 2 adapts Barbiero and Ferrari's 2015
modification of the 'GenOrd' package <DOI:10.1002/asmb.2072> and performs best under the
opposite scenarios. The optional error loop may be used to improve the accuracy of the
final correlation matrix. The package also contains functions to calculate the
standardized cumulants of continuous mixture distributions, check parameter inputs,
calculate feasible correlation boundaries, and summarize and plot simulated variables.

Allison Fialkowski

SimCorrMix

Simulation of Correlated Data with Multiple Variable Types
Including Continuous and Count Mixture Distributions

maxcount_support function

This function calculates the maximum support value for count variables by extending the method of Barbiero &amp;
 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
 (<code>pois_eps</code> or <code>nb_eps</code>). 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 <code><a rd-options='SimCorrMix' href='intercorr2'>intercorr2</a></code> and <code><a rd-options='SimCorrMix' href='corrvar2'>corrvar2</a></code> and
 would not ordinarily be called by the user.

maxcount_support: Calculate Maximum Support Value for Count Variables: Correlation Method 2

Description

Usage

Arguments

Value

References

See Also