ophi2poly {CorrToolBox}

Computation of the Polychoric Correlation from the Ordinal Phi Coefficient

Description

This function computes the polychoric correlation between two continuous variables given the correlation after ordinalization of both variables (ordinal phi coefficient) as seen in Demirtas et al. (2016). Before computation of the polychoric correlation, the specified ordinal phi coefficient is compared to the lower and upper correlation bounds of the two ordinal variables using the generate, sort and correlate (GSC) algorithm in Demirtas and Hedeker (2011).

Usage

ophi2poly(ophicoef, dist1, dist2)

Arguments

ophicoef

The ordinal phi coefficient.

dist1

A list of length 3 containing the skewness, excess kurtosis, and a numeric vector of marginal probabilities after dichotomization for the first continuous variable with names skewness, exkurtosis, and p, respectively.

dist2

A list of length 3 containing the skewness, excess kurtosis, and a numeric vector of marginal probabilities after dichotomization for the second continuous variable with names skewness, exkurtosis, and p, respectively.

Value

The polychoric correlation.

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.

Demirtas, H. and Hedeker, D. (2011). A practical way for computing approximate lower and upper correlation bounds. The American Statistician, 65(2), 104-109.

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

See Also

corrZ2corrY, ophi2corrZ, mps2cps

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)

ophi2poly(ophicoef=-0.7, 
          dist1=list(skewness=y1.skew, exkurtosis=y1.exkurt, p=c(0.4, 0.3, 0.2, 0.1)),
          dist2=list(skewness=y2.skew, exkurtosis=y2.exkurt, p=c(0.2, 0.2, 0.6)))

ophi2poly(ophicoef=0.2, 
          dist1=list(skewness=y1.skew, exkurtosis=y1.exkurt, p=c(0.1, 0.1, 0.1, 0.7)),
          dist2=list(skewness=y2.skew, exkurtosis=y2.exkurt, p=c(0.8, 0.1, 0.1)))