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