corrZ2ophi {CorrToolBox}

Computation of the Ordinal Phi Coefficient from the Correlation of Bivariate Standard Normal Variables

Description

This is an intermediate function that utilizes mps2cps to transform the specified marginal probabilities into cumulative probabilities and uses the contord function in the GenOrd package to compute the ordinal phi coefficient derived from discretizing bivariate standard normal variables.

Usage

corrZ2ophi(corrZ, p1, p2)

Arguments

corrZ

The correlation of two standard normal variables.

p1

A numeric vector containing marginal probabilities defining categories for the first ordinal variable.

p2

A numeric vector containing marginal probabilities defining categories for the second ordinal variable.

Value

The ordinal phi coefficient.

References

Demirtas, H., Ahmadian, R., Atis, S., Can, F.E., and Ercan, I. (2016). A nonnormal look at polychoric correlations: modeling the change in correlations before and after discretization. Computational Statistics, 31(4), 1385-1401.

Ferrari, P.A. and Barbiero, A. (2012). Simulating ordinal data. Multivariate Behavioral Research, 47(4), 566-589.

See Also

mps2cps, poly2ophi

Examples

set.seed(567)
library(moments)

y1<-rweibull(n=100000, scale=1, shape=3.6)
y1.skew<-round(skewness(y1), 5)
y1.exkurt<-round(kurtosis(y1)-3, 5)

gaussmix <- function(n,m1,m2,s1,s2,pi) {
  I <- runif(n)<pi
  rnorm(n,mean=ifelse(I,m1,m2),sd=ifelse(I,s1,s2))
}
y2<-gaussmix(n=100000, m1=0, s1=1, m2=2, s2=1, pi=0.3)
y2.skew<-round(skewness(y2), 5)
y2.exkurt<-round(kurtosis(y2)-3, 5)

corrZ2ophi(corrZ=0.502, p1=c(0.4, 0.3, 0.2, 0.1), p2=c(0.2, 0.2, 0.6))