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
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
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).
the method used to generate the continuous variables. "Fleishman" uses Fleishman's third-order polynomial transformation and "Polynomial" uses Headrick's fifth-order transformation.
a matrix with each row a vector of constants c0, c1, c2, c3 (if
a matrix of target correlations among continuous variables, does not have to be symmetric
the intermediate matrix of correlations with the same dimensions as
Please see additional references for
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.
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