findintercorr_pois: Calculate Intermediate MVN Correlation for Poisson Variables:...

In SimMultiCorrData: Simulation of Correlated Data with Multiple Variable Types

Description

This function calculates a k_pois x k_pois intermediate matrix of correlations for the Poisson variables using the method of Yahav & Shmueli (2012, doi: 10.1002/asmb.901). The intermediate correlation between Z1 and Z2 (the standard normal variables used to generate the Poisson 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) ρ_{y1,y2} are simulated. Then the intermediate correlation is found as follows:

ρ_{z1,z2} = (1/b) * log((ρ_{y1,y2} - c)/a)

, where a = -(maxcor * mincor)/(maxcor + mincor), b = log((maxcor + a)/a), and c = -a. The function adapts code from Amatya & Demirtas' (2016) package PoisNor-package by:

1) allowing specifications for the number of random variates and the seed for reproducibility

2) providing the following checks: if ρ_{z1,z2} >= 1, ρ_{z1,z2} is set to 0.99; if ρ_{z1,z2} <= -1, ρ_{z1,z2} is set to -0.99.

The function is used in findintercorr and rcorrvar. This function would not ordinarily be called by the user.

Note: The method used here is also used in the packages PoisBinOrdNor-package and PoisBinOrdNonNor-package by Demirtas et al. (2017), but without my modifications.

Usage

findintercorr_pois(rho_pois, lam, nrand = 100000, seed = 1234)

Arguments

rho_pois	a k_pois x k_pois matrix of target correlations
lam	a vector of lambda (> 0) constants for the Poisson variables (see Poisson)
nrand	the number of random numbers to generate in calculating the bound (default = 10000)
seed	the seed used in random number generation (default = 1234)

Value

the k_pois x k_pois intermediate correlation matrix for the Poisson variables

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): 3129-39. doi: 10.1080/00949655.2014.953534.

Amatya A & Demirtas H (2016). PoisNor: Simultaneous Generation of Multivariate Data with Poisson and Normal Marginals. R package version 1.1. https://CRAN.R-project.org/package=PoisNor

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

Demirtas H, Hu Y, & Allozi R (2017). PoisBinOrdNor: Data Generation with Poisson, Binary, Ordinal and Normal Components. R package version 1.4. https://CRAN.R-project.org/package=PoisBinOrdNor

Demirtas H, Nordgren R, & Allozi R (2017). PoisBinOrdNonNor: Generation of Up to Four Different Types of Variables. R package version 1.3. https://CRAN.R-project.org/package=PoisBinOrdNonNor

Frechet M. Sur les tableaux de correlation dont les marges sont donnees. Ann. l'Univ. Lyon SectA. 1951;14:53-77.

Hoeffding W. Scale-invariant correlation theory. In: Fisher NI, Sen PK, editors. The collected works of Wassily Hoeffding. New York: Springer-Verlag; 1994. p. 57-107.

Yahav I & Shmueli G (2012). On Generating Multivariate Poisson Data in Management Science Applications. Applied Stochastic Models in Business and Industry, 28(1): 91-102. doi: 10.1002/asmb.901.

See Also

PoisNor-package, findintercorr_nb, findintercorr_pois_nb, findintercorr, rcorrvar

SimMultiCorrData documentation built on May 2, 2019, 9:50 a.m.