ophi2corrZ {CorrToolBox}

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

Description

This is an intermediate function that transforms marginal probabilities into cumulative probabilities and uses the ordcont function in the GenOrd package to compute the correlation of bivariate standard normal variables from the ordinal phi coefficient.

Usage

ophi2corrZ(ophi, p1, p2)

Arguments

ophi

The ordinal phi coefficient.

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 correlation of standard normal variables.

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, ophi2poly

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)

ophi2corrZ(ophi=-0.7, p1=c(0.4, 0.3, 0.2, 0.1), p2=c(0.2, 0.2, 0.6))