psych (version 1.0-17)

# phi2poly: Convert a phi coefficient to a polychoric correlation

## Description

Given a phi coefficient (a Pearson r calculated on two dichotomous variables), and the marginal frequencies, what is the corresponding estimate of the polychoric correlation?

## Usage

`phi2poly(ph, cp, cc)`

## Arguments

ph
phi
cp
probability of the predictor -- the so called selection ratio
cc
probability of the criterion -- the so called success rate.

## Value

• a polychoric correlation

## Details

Uses John Fox's polycor function.

`polychor.matrix`

## Examples

Run this code
``````##---- Should be DIRECTLY executable !! ----
##-- ==>  Define data, use random,
##--	or do  help(data=index)  for the standard data sets.

## The function is currently defined as
function(ph,cp,cc) {
require(polycor)
#ph is the phi coefficient
#cp is the selection ratio of the predictor
#cc is the success rate of the criterion
r.marg<-rep(0,2)
c.marg<- rep(0,2)
p<-array(rep(0,4),dim=c(2,2))
r.marg[1]<- cp
r.marg[2]<- 1 -cp
c.marg[1]<- cc
c.marg[2]<- 1-cc

p[1,1]<- r.marg[1]*c.marg[1]+ ph*sqrt(prod(r.marg,c.marg))
p[2,2]<- r.marg[2]*c.marg[2]+ ph*sqrt(prod(r.marg,c.marg))
p[1,2]<- r.marg[1]*c.marg[2]- ph*sqrt(prod(r.marg,c.marg))
p[2,1]<- r.marg[2]*c.marg[1]- ph*sqrt(prod(r.marg,c.marg))

result<-polychor(p )
return(result)}``````

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