rho_M1Y

a vector of mixing probabilities that sum to 1 for component distributions of \(M1\)

mix_pis

a vector of means for component distributions of \(M1\)

mix_mus

a vector of standard deviations for component distributions of \(M1\)

mix_sigmas

a vector of correlations between the components of \(M1\) and \(Y\); i.e.,
<code>p_M1Y[1]</code> is the correlation between the 1st component of \(M1\) and \(Y\)

p_M1Y

This function approximates the expected correlation between a continuous mixture variables \(M1\) and another random
 variable \(Y\) based on the mixing proportions, component means, and component standard deviations of \(M1\) and correlations
 between components of \(M1\) and \(Y\). The equations can be found in the Expected Cumulants and Correlations for
 Continuous Mixture Variables vignette. This function can be used to see what combination of correlations between components
 of \(M1\) and \(Y\) gives a desired correlation between \(M1\) and \(Y\).

correlation

mixture

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.

rho_M1Y: Approximate Correlation between Continuous Mixture Variable M1 and Random Variable Y

Description

Usage

Arguments

Value

References

See Also

Examples