Headrick.dist

<p>Selected symmetrical and asymmetrical theoretical densities with their associated values
of skewness (gamma1), standardized kurtosis (gamma2), and standardized fifth (gamma3) and
sixth (gamma4) cumulants.  Constants were calculated by Headrick using his fifth-order
polynomial transformation and given in his Table 1 (2002, p. 691-2, 10.1016/S0167-9473(02)00072-5).  Note that the standardized cumulants for the Gamma(10, 10)
distribution do not arise from using \(\alpha = 10,\ \beta = 10\).  Therefore, either there is a typo in the table or
Headrick used a different parameterization.</p>

datasets

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

Headrick.dist function

<p>An object of class <code>"data.frame"</code>; Colnames are distribution names; rownames are
standardized cumulant names followed by c0, ..., c5.</p>

Headrick.dist: Examples of Constants Calculated by Headrick's Fifth-Order Polynomial Transformation

Description

Usage

Arguments

Format

References

Examples