R: Calculate Intermediate MVN Correlation for Continuous...

findintercorr_cont {SimMultiCorrData}

R Documentation

Calculate Intermediate MVN Correlation for Continuous Variables Generated by Polynomial Transformation

Description

This function finds the roots to the equations in intercorr_fleish or intercorr_poly using nleqslv. It is used in findintercorr and findintercorr2 to find the intermediate correlation for standard normal random variables which are used in Fleishman's Third-Order (doi: 10.1007/BF02293811) or Headrick's Fifth-Order (doi: 10.1016/S0167-9473(02)00072-5) Polynomial Transformation. It works for two or three variables in the case of method = "Fleishman", or two, three, or four variables in the case of method = "Polynomial". Otherwise, Headrick & Sawilowsky (1999, doi: 10.1007/BF02294317) recommend using the technique of Vale & Maurelli (1983, doi: 10.1007/BF02293687), in which the intermediate correlations are found pairwise and then eigen value decomposition is used on the intermediate correlation matrix. This function would not ordinarily be called by the user.

Usage

findintercorr_cont(method = c("Fleishman", "Polynomial"), constants, rho_cont)

Arguments

`method`	the method used to generate the continuous variables. "Fleishman" uses Fleishman's third-order polynomial transformation and "Polynomial" uses Headrick's fifth-order transformation.
`constants`	a matrix with either 2, 3, or 4 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`	a matrix of target correlations among continuous variables; if `nrow(rho_cont) = 1`, it represents a pairwise correlation; if `nrow(rho_cont) = 2, 3, or 4`, it represents a correlation matrix between two, three, or four variables

Value

a list containing the results from nleqslv

References

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

Hasselman B (2018). nleqslv: Solve Systems of Nonlinear Equations. R package version 3.3.2. https://CRAN.R-project.org/package=nleqslv

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.