intercor.NN: Computes the subset of the intermediate correlation matrix that is pertinent to the continuous pairs

Description

This function computes the submatrix of the intermediate correlation matrix of the multivariate normal distribution. It is relevant to the continuous part of the data.

Usage

intercor.NN(pmat, cmat)

Arguments

pmat

a n2x4 matrix where each row includes the four coefficients (a,b,c,d) of the Fleishman's system.

cmat

a n2xn2 matrix of specified correlations for the continuous part.

Value

Returns an intermediate matrix of size n2xn2

Details

Fleishman polynomials is a method to generate real-life non-normal distributions of variables by using their first four moments. It is based on the polynomial transformation, \(Y = a + bZ + cZ^2 + dZ^3\), where Z follows a standard normal distribution and Y is standardized (zero mean and unit variance).

Normal-Normal correlation for a given continuous pair can be calculated by solving the following equation.

\(r_{Y_1Y_2} = r_{Z_1Z_2}(b_1b_2+3b_1d_2+3d_1b_2+9d_1d_2) + r_{Z_1Z_2}^2(2c_1c_2)+r_{Z_1Z_2}^3(6d_1d_2)\)

References

Yahav, I. and Shmueli, G. (2012). On generating multivariate poisson data in management science applications. Applied Stochastic Models in Business and Industry, 28(1), 91-102.

Examples

Run this code

# NOT RUN {
pmat = matrix(c(
  0.1148643, 1.0899150, -0.1148643, -0.0356926,
  -0.0488138, 0.9203374,  0.0488138,  0.0251256,
  -0.2107427, 1.0398224,  0.2107427, -0.0293247), nrow=3, byrow=TRUE)
cmat = matrix(c(
  1.000,  0.100, 0.354,
  0.100,  1.000, 0.386,
  0.354,  0.386, 1.000),nrow=3,byrow=TRUE)

intercor.NN(pmat,cmat)
# }

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