findintercorr_nb

a <code>k_nb x k_nb</code> matrix of target correlations

rho_nb

a vector of size parameters for the Negative Binomial variables (see <code><a rd-options="stats" href="/link/NegBinomial?package=SimMultiCorrData&version=0.2.2&to=stats" data-mini-rdoc="stats::NegBinomial">NegBinomial</a></code>)

size

a vector of success probability parameters

prob

a vector of mean parameters (*Note: either <code>prob</code> or <code>mu</code> should be supplied for all Negative Binomial variables,
not a mixture; default = NULL)

the number of random numbers to generate in calculating the bound (default = 10000)

nrand

the seed used in random number generation (default = 1234)

seed

This function calculates a <code>k_nb x k_nb</code> intermediate matrix of correlations for the Negative Binomial variables by
 extending the method of Yahav &amp; Shmueli (2012, 10.1002/asmb.901). The intermediate correlation between Z1 and Z2 (the
 standard normal variables used to generate the Negative Binomial variables Y1 and Y2 via the inverse cdf method) is
 calculated using a logarithmic transformation of the target correlation. First, the upper and lower Frechet-Hoeffding bounds
 (mincor, maxcor) on $\rho_{y1,y2}$ are simulated. Then the intermediate correlation is found as follows:
 $$\rho_{z1,z2} = (1/b) * log((\rho_{y1,y2} - c)/a)$$, where $a = -(maxcor * mincor)/(maxcor + mincor)$,
 $b = log((maxcor + a)/a)$, and $c = -a$. The function adapts code from Amatya &amp; Demirtas' (2016) package
 <code><a rd-options="PoisNor" href="/link/PoisNor-package?package=SimMultiCorrData&version=0.2.2&to=PoisNor" data-mini-rdoc="PoisNor::PoisNor-package">PoisNor-package</a></code> by:
1) allowing specifications for the number of random variates and the seed for reproducibility
2) providing the following checks: if $\rho_{z1,z2}$ &gt;= 1, $\rho_{z1,z2}$ is set to 0.99; if $\rho_{z1,z2}$ &lt;= -1,
 $\rho_{z1,z2}$ is set to -0.99
3) simulating Negative Binomial variables.
The function is used in <code><a rd-options="SimMultiCorrData" href="/link/findintercorr?package=SimMultiCorrData&version=0.2.2&to=SimMultiCorrData" data-mini-rdoc="SimMultiCorrData::findintercorr">findintercorr</a></code> and <code><a rd-options="SimMultiCorrData" href="/link/rcorrvar?package=SimMultiCorrData&version=0.2.2&to=SimMultiCorrData" data-mini-rdoc="SimMultiCorrData::rcorrvar">rcorrvar</a></code>.
 This function would not ordinarily be called by the user.

correlation

method

binomial

negative

intermediate

Generate continuous (normal or non-normal), binary, ordinal, and count (Poisson or Negative
Binomial) variables with a specified correlation matrix. It can also produce a single continuous
variable. This package can be used to simulate data sets that mimic real-world situations (i.e.
clinical or genetic data sets, plasmodes). All variables are generated from standard normal
variables with an imposed intermediate correlation matrix. Continuous variables are simulated
by specifying mean, variance, skewness, standardized kurtosis, and fifth and sixth standardized
cumulants using either Fleishman's third-order (<DOI:10.1007/BF02293811>) or Headrick's
fifth-order (<DOI:10.1016/S0167-9473(02)00072-5>) polynomial transformation. Binary and
ordinal variables are simulated using a modification of the ordsample() function from 'GenOrd'.
Count variables are simulated using the inverse cdf method. There are two simulation pathways
which differ primarily according to the calculation of the intermediate correlation matrix. In
Correlation Method 1, the intercorrelations involving count variables are determined using a
simulation based, logarithmic correlation correction (adapting Yahav and Shmueli's 2012 method,
<DOI:10.1002/asmb.901>). In Correlation Method 2, the count variables are treated as ordinal
(adapting Barbiero and Ferrari's 2015 modification of GenOrd, <DOI:10.1002/asmb.2072>).
There is an optional error loop that corrects the final correlation matrix to be within a
user-specified precision value of the target matrix. The package also includes functions to
calculate standardized cumulants for theoretical distributions or from real data sets, check
if a target correlation matrix is within the possible correlation bounds (given the distributions
of the simulated variables), summarize results (numerically or graphically), to verify valid power
method pdfs, and to calculate lower standardized kurtosis bounds.

Allison Fialkowski

SimMultiCorrData

Simulation of Correlated Data with Multiple Variable Types

findintercorr_nb function

a vector of size parameters for the Negative Binomial variables (see <code><a rd-options='stats' href='NegBinomial'>NegBinomial</a></code>)

This function calculates a <code>k_nb x k_nb</code> intermediate matrix of correlations for the Negative Binomial variables by
 extending the method of Yahav &amp; Shmueli (2012, 10.1002/asmb.901). The intermediate correlation between Z1 and Z2 (the
 standard normal variables used to generate the Negative Binomial variables Y1 and Y2 via the inverse cdf method) is
 calculated using a logarithmic transformation of the target correlation. First, the upper and lower Frechet-Hoeffding bounds
 (mincor, maxcor) on $\rho_{y1,y2}$ are simulated. Then the intermediate correlation is found as follows:
 $$\rho_{z1,z2} = (1/b) * log((\rho_{y1,y2} - c)/a)$$, where $a = -(maxcor * mincor)/(maxcor + mincor)$,
 $b = log((maxcor + a)/a)$, and $c = -a$. The function adapts code from Amatya &amp; Demirtas' (2016) package
 <code><a rd-options='PoisNor' href='PoisNor-package'>PoisNor-package</a></code> by:
1) allowing specifications for the number of random variates and the seed for reproducibility
2) providing the following checks: if $\rho_{z1,z2}$ &gt;= 1, $\rho_{z1,z2}$ is set to 0.99; if $\rho_{z1,z2}$ &lt;= -1,
 $\rho_{z1,z2}$ is set to -0.99
3) simulating Negative Binomial variables.
The function is used in <code><a rd-options='SimMultiCorrData' href='findintercorr'>findintercorr</a></code> and <code><a rd-options='SimMultiCorrData' href='rcorrvar'>rcorrvar</a></code>.
 This function would not ordinarily be called by the user.

State of Data and AI Literacy Report 2025

findintercorr_nb: Calculate Intermediate MVN Correlation for Negative Binomial Variables: Correlation Method 1

Description

Usage

Arguments

Value

References

See Also