R: Calculate Intermediate MVN Correlation to Generate Variables...

ordnorm {SimMultiCorrData}

R Documentation

Calculate Intermediate MVN Correlation to Generate Variables Treated as Ordinal

Description

This function calculates the intermediate MVN correlation needed to generate a variable described by a discrete marginal distribution and associated finite support. This includes ordinal (r >= 2 categories) variables or variables that are treated as ordinal (i.e. count variables in the Barbiero & Ferrari, 2015 method used in rcorrvar2, doi: 10.1002/asmb.2072). The function is a modification of Barbiero & Ferrari's ordcont function in GenOrd-package. It works by setting the intermediate MVN correlation equal to the target correlation and updating each intermediate pairwise correlation until the final pairwise correlation is within epsilon of the target correlation or the maximum number of iterations has been reached. This function uses contord to calculate the ordinal correlation obtained from discretizing the normal variables generated from the intermediate correlation matrix. The ordcont has been modified in the following ways:

1) the initial correlation check has been removed because it is assumed the user has done this before simulation using valid_corr or valid_corr2

2) the final positive-definite check has been removed

3) the intermediate correlation update function was changed to accomodate more situations, and

4) a final "fail-safe" check was added at the end of the iteration loop where if the absolute error between the final and target pairwise correlation is still > 0.1, the intermediate correlation is set equal to the target correlation.

This function would not ordinarily be called by the user. Note that this will return a matrix that is NOT positive-definite because this is corrected for in the simulation functions rcorrvar and rcorrvar2 using the method of Higham (2002) and the nearPD function.

Usage

ordnorm(marginal, rho, support = list(), epsilon = 0.001, maxit = 1000)

Arguments

`marginal`	a list of length equal to the number of variables; the i-th element is a vector of the cumulative probabilities defining the marginal distribution of the i-th variable; if the variable can take r values, the vector will contain r - 1 probabilities (the r-th is assumed to be 1)
`rho`	the target correlation matrix
`support`	a list of length equal to the number of variables; the i-th element is a vector of containing the r ordered support values; if not provided (i.e. support = list()), the default is for the i-th element to be the vector 1, ..., r
`epsilon`	the maximum acceptable error between the final and target correlation matrices (default = 0.001); smaller epsilons take more time
`maxit`	the maximum number of iterations to use (default = 1000) to find the intermediate correlation; the correction loop stops when either the iteration number passes maxit or epsilon is reached

Value

A list with the following components:

SigmaC the intermediate MVN correlation matrix

rho0 the calculated final correlation matrix generated from SigmaC

rho the target final correlation matrix

niter a matrix containing the number of iterations required for each variable pair

maxerr the maximum final error between the final and target correlation matrices

References

Barbiero A, Ferrari PA (2015). Simulation of correlated Poisson variables. Applied Stochastic Models in Business and Industry, 31: 669-80. doi: 10.1002/asmb.2072.

Barbiero A, Ferrari PA (2015). GenOrd: Simulation of Discrete Random Variables with Given Correlation Matrix and Marginal Distributions. R package version 1.4.0. https://CRAN.R-project.org/package=GenOrd