intercorr_poly {SimMultiCorrData}

Headrick's Fifth-Order Polynomial Transformation Intermediate Correlation Equations

Description

This function contains Headrick's fifth-order polynomial transformation intermediate correlation equations (2002, doi: 10.1016/S0167-9473(02)00072-5). It is used in findintercorr and findintercorr2 to find the intermediate correlation for standard normal random variables which are used in the Headrick polynomial transformation. It can be used to verify a set of constants and an intermediate correlation satisfy the equations for the desired post-transformation correlation. It works for two, three, or four variables. Headrick recommended using the technique of Vale & Maurelli (1983, doi: 10.1007/BF02293687), in the case of more than 4 variables, in which the intermediate correlations are found pairwise and then eigen value decomposition is used on the correlation matrix. Note that there exist solutions that yield invalid power method pdfs (see power_norm_corr, pdf_check). This function would not ordinarily be called by the user.

Usage

intercorr_poly(r, c, a)

Arguments

r

either a scalar, in which case it represents pairwise intermediate correlation between standard normal variables, or a vector of 3 values, in which case:

r[1]*r[2] = \rho_{z1,z2},\ r[1]*r[3] = \rho_{z1,z3},\ r[2]*r[3] = \rho_{z2,z3}

or a vector of 4 values, in which case:

r0 = r[5]*r[6],\ r0*r[1]*r[2] = \rho_{z1,z2},\ r0*r[1]*r[3] = \rho_{z1,z3}

r0*r[2]*r[3] = \rho_{z2,z3},\ r0*r[1]*r[4] = \rho_{z1,z4},\ r0*r[2]*r[4] = \rho_{z2,z4},

r0*r[3]*r[4] = \rho_{z3,z4}

c

a matrix with either 2, 3, or 4 rows, each a vector of constants c0, c1, c2, c3, like that returned by find_constants

a

a matrix of target correlations among continuous variables; if nrow(a) = 1, it represents a pairwise correlation; if nrow(a) = 2, 3, or 4, it represents a correlation matrix between two, three, or four variables

Value

a list of length 1 for pairwise correlations, length 3 for three variables, or length 6 for four variables; if the inputs satisfy the equations, returns 0 for all list elements

References

Please see references for findintercorr_cont.

See Also

poly, power_norm_corr, pdf_check, find_constants