CorPolychor {DescTools}  R Documentation 
Polychoric Correlation
Description
Computes the polychoric correlation (and its standard error) between two ordinal variables or from their contingency table, under the assumption that the ordinal variables dissect continuous latent variables that are bivariate normal. Either the maximumlikelihood estimator or a (possibly much) quicker “twostep” approximation is available. For the ML estimator, the estimates of the thresholds and the covariance matrix of the estimates are also available.
Usage
CorPolychor(x, y, ML = FALSE, control = list(), std.err = FALSE, maxcor=.9999)
## S3 method for class 'CorPolychor'
print(x, digits = max(3, getOption("digits")  3), ...)
Arguments
x 
a contingency table of counts or an ordered categorical variable; the latter can be numeric, logical, a factor, or an ordered factor, but if a factor, its levels should be in proper order. 
y 
if 
ML 
if 
control 
optional arguments to be passed to the 
std.err 
if 
maxcor 
maximum absolute correlation (to insure numerical stability). 
digits 
integer, determining the number of digits used to format the printed result 
... 
not used 
Value
If std.err
is TRUE
,
returns an object of class "polycor"
with the following components:
type 
set to 
rho 
the CorPolychoric correlation. 
var 
the estimated variance of the correlation, or, for the ML estimate, the estimated covariance matrix of the correlation and thresholds. 
n 
the number of observations on which the correlation is based. 
chisq 
chisquare test for bivariate normality. 
df 
degrees of freedom for the test of bivariate normality. 
ML 

Othewise, returns the polychoric correlation.
Note
This is a verbatim copy from polchor function in the package polycor.
Author(s)
John Fox jfox@mcmaster.ca
References
Drasgow, F. (1986) CorPolychoric and polyserial correlations. Pp. 68–74 in S. Kotz and N. Johnson, eds., The Encyclopedia of Statistics, Volume 7. Wiley.
Olsson, U. (1979) Maximum likelihood estimation of the CorPolychoric correlation coefficient. Psychometrika 44, 443460.
See Also
hetcor
, polyserial
, print.CorPolychor
, optim
Examples
set.seed(12345)
z < RndPairs(1000, 0.6)
x < z[,1]
y < z[,2]
cor(x, y) # sample correlation
x < cut(x, c(Inf, .75, Inf))
y < cut(y, c(Inf, 1, .5, 1.5, Inf))
CorPolychor(x, y) # 2step estimate
CorPolychor(x, y, ML=TRUE, std.err=TRUE) # ML estimate