Description Usage Arguments Value References See Also

View source: R/intercorr_pois.R

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) on *ρ_{Y1, Y2}* are simulated. Then the intermediate correlation is found as follows:

*ρ_{Z1, Z2} = \frac{1}{b} * log(\frac{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 `Sigma_(Z1, Z2)`

> 1, `Sigma_(Z1, Z2)`

is set to 1; if `Sigma_(Z1, Z2)`

< -1,
`Sigma_(Z1, Z2)`

is set to -1

3) simulating regular and zero-inflated Poisson variables.

The function is used in `intercorr`

and `corrvar`

and would not ordinarily be called by the user.

1 2 | ```
intercorr_pois(rho_pois = NULL, lam = NULL, p_zip = 0, nrand = 100000,
seed = 1234)
``` |

`rho_pois` |
a |

`lam` |
a vector of lambda (mean > 0) constants for the regular and zero-inflated Poisson variables (see |

`p_zip` |
a vector of probabilities of structural zeros (not including zeros from the Poisson distribution) for the
zero-inflated Poisson variables (see |

`nrand` |
the number of random numbers to generate in calculating the bound (default = 10000) |

`seed` |
the seed used in random number generation (default = 1234) |

the `k_pois x k_pois`

intermediate correlation matrix for the Poisson variables

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.

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

Frechet M (1951). Sur les tableaux de correlation dont les marges sont donnees. Ann. l'Univ. Lyon SectA, 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.

Yee TW (2018). VGAM: Vector Generalized Linear and Additive Models. R package version 1.0-5. https://CRAN.R-project.org/package=VGAM.

`intercorr_nb`

, `intercorr_pois_nb`

,
`intercorr`

, `corrvar`

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