Generation of up to Four Different Types of Variables

Description

Simultaneous generation of a chosen number of count, binary, ordinal, and continuous random variables, with specified correlations and marginal distributions. Throughout the package, the word 'Poisson' is used to imply count data under the assumption of Poisson distribution; and continuous variables can take any shape allowed by Fleishman polynomials.

Generation of a chosen number of count, binary, ordinal, and continuous (via Fleishman polynomials) random variables, with specified correlations and marginal properties. The correlation matrix and the generated data follow the order of Poisson, binary, ordinal and continuous.

Details

This package consists of five public functions. The function check.params validates the input parameters to avoid obvious specification errors of the marginal parameters. The function validate.cor.mat validates an input target correlation matrix to make sure that it is a legitimate correlation matrix, and then calls lower.upper.cors with the rest of the input parameters to generate approximate maximum and minimum feasible bounds, and then checks that each entry is within its bounds. The function find.cor.mat.star creates the intermediate correlation matrix. Finally, given the output from find.cor.mat.star along with the other variable specifications, the function genPBONN generates the simultaneous random data, following the target correlation matrix and the marginal input parameters.

Note

The approximation used to find the correlation for Poisson variables is not very accurate once lambda is less than 1, and becomes less accurate as lambda gets closer to 0.

A flag is used to specify if ordinal probabilities are cumulative–default is FALSE.

Binary variables can be listed separately or combined with ordinal variables–the results will be equivalent. Any variables listed as ordinal are affected by the cumulative flag.

Author(s)

Hakan Demirtas, Rachel Nordgren, Rawan Allozi

Maintainer: Rawan Allozi <ralloz2@uic.edu>

References

Amatya, A. & Demirtas, H. (2015) Simultaneous generation of multivariate mixed data with Poisson and normal marginals. Journal of Statistical Computation and Simulation 85:15, 3129–3139.

Demirtas, H. & Hedeker, D. (2011) A practical way for computing approximate lower and upper correlation bounds. American Statistician 65:2, 104–109.

Demirtas, H., Hedeker, D. & Mermelstein, R. J. (2012) Simulation of massive public health data by power polynomials. Statistics in Medicine 31:27, 3337–3346.

Demirtas, H. (2014). Joint generation of binary and nonnormal continuous data. Journal of Biometrics and Biostatistics 5:3:1000199, 1–9.

Demirtas, H. & Hedeker, D. (2016). Computing the point-biserial correlation under any underlying continuous distribution. Forthcoming in Communications in Statistics– Simulation and Computation.

Results