findintercorr_cont: Calculate Intermediate MVN Correlation for Continuous...
In SimMultiCorrData: Simulation of Correlated Data with Multiple Variable Types

Description Usage Arguments Value References See Also

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.

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

`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

a list containing the results from nleqslv

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.

Vale CD & Maurelli VA (1983). Simulating Multivariate Nonnormal Distributions. Psychometrika, 48, 465-471. doi: 10.1007/BF02293687.

poly, fleish, power_norm_corr, pdf_check, find_constants, intercorr_fleish,
intercorr_poly, nleqslv