# intercorr_cont: Calculate Intermediate MVN Correlation for Continuous... In SimCorrMix: Simulation of Correlated Data with Multiple Variable Types Including Continuous and Count Mixture Distributions

## Description

This function finds 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 method (PMT) using `nleqslv`. It is used in `intercorr` and `intercorr2` and would not ordinarily be called by the user. The correlations are found pairwise so that eigen-value or principal components decomposition should be done on the resulting `Sigma` matrix. The Comparison of Correlation Methods 1 and 2 vignette contains the equations which were derived by Headrick and Sawilowsky (doi: 10.1007/BF02294317) or Headrick (doi: 10.1016/S0167-9473(02)00072-5).

## Usage

 ```1 2``` ```intercorr_cont(method = c("Fleishman", "Polynomial"), constants = NULL, rho_cont = NULL) ```

## 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 each row 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, does not have to be symmetric

## Value

the intermediate matrix of correlations with the same dimensions as `rho_cont`

## References

Please see additional references for `SimCorrMix`.

Fialkowski AC (2018). SimMultiCorrData: Simulation of Correlated Data with Multiple Variable Types. R package version 0.2.2. https://CRAN.R-project.org/package=SimMultiCorrData.

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, 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.

`intercorr`, `intercorr2`, `nleqslv`