R: Calculate Intermediate MVN Correlation for Continuous -...

findintercorr_cont_pois {SimMultiCorrData}

R Documentation

Calculate Intermediate MVN Correlation for Continuous - Poisson Variables: Correlation Method 1

Description

This function calculates a k_cont x k_pois intermediate matrix of correlations for the k_cont continuous and k_pois Poisson variables. It extends the method of Amatya & Demirtas (2015, doi: 10.1080/00949655.2014.953534) to continuous variables generated using Headrick's fifth-order polynomial transformation. Here, the intermediate correlation between Z1 and Z2 (where Z1 is the standard normal variable transformed using Headrick's fifth-order or Fleishman's third-order method to produce a continuous variable Y1, and Z2 is the standard normal variable used to generate a Poisson variable via the inverse cdf method) is calculated by dividing the target correlation by a correction factor. The correction factor is the product of the upper Frechet-Hoeffding bound on the correlation between a Poisson variable and the normal variable used to generate it (see chat_pois) and the power method correlation (described in Headrick & Kowalchuk, 2007, doi: 10.1080/10629360600605065) between Y1 and Z1. The function is used in findintercorr and rcorrvar. This function would not ordinarily be called by the user.

Usage

findintercorr_cont_pois(method, constants, rho_cont_pois, lam, nrand = 100000,
  seed = 1234)

Arguments

`method`	the method used to generate the `k_cont` continuous variables. "Fleishman" uses a third-order polynomial transformation and "Polynomial" uses Headrick's fifth-order transformation.
`constants`	a matrix with `k_cont` rows, each a vector of constants c0, c1, c2, c3 (if `method` = "Fleishman") or c0, c1, c2, c3, c4, c5 (if `method` = "Polynomial"), like that returned by `find_constants`
`rho_cont_pois`	a `k_cont x k_pois` matrix of target correlations among continuous and Poisson variables
`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

a k_cont x k_pois matrix whose rows represent the k_cont continuous variables and columns represent the k_pois 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.

Demirtas H & Hedeker D (2011). A practical way for computing approximate lower and upper correlation bounds. American Statistician, 65(2): 104-109. doi: 10.1198/tast.2011.10090.

Fleishman AI (1978). A Method for Simulating Non-normal Distributions. Psychometrika, 43, 521-532. doi: 10.1007/BF02293811.

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

Headrick TC (2002). Fast Fifth-order Polynomial Transforms for Generating Univariate and Multivariate Non-normal Distributions. Computational Statistics & Data Analysis, 40(4):685-711. doi: 10.1016/S0167-9473(02)00072-5. (ScienceDirect)

Headrick TC (2004). On Polynomial Transformations for Simulating Multivariate Nonnormal Distributions. Journal of Modern Applied Statistical Methods, 3(1), 65-71. doi: 10.22237/jmasm/1083370080.

Headrick TC, Kowalchuk RK (2007). The Power Method Transformation: Its Probability Density Function, Distribution Function, and Its Further Use for Fitting Data. Journal of Statistical Computation and Simulation, 77, 229-249. doi: 10.1080/10629360600605065.

Headrick TC, Sawilowsky SS (1999). Simulating Correlated Non-normal Distributions: Extending the Fleishman Power Method. Psychometrika, 64, 25-35. doi: 10.1007/BF02294317.

Headrick TC, Sheng Y, & Hodis FA (2007). Numerical Computing and Graphics for the Power Method Transformation Using Mathematica. Journal of Statistical Software, 19(3), 1 - 17. doi: 10.18637/jss.v019.i03.

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.