R help - Nov 2004 - Tetrachoric and polychoric ceofficients (for sem) - any tips?

About two years ago there was a thread about this which suggested that at 
that time nobody had these coefficients ready to go.
(a) has anyone in the meanwhile programmed them?
(b) I think I can see how to do the tetrachoric one with mvtnorm on similar 
lines to an example on the help page so will try that if nobody else 
already has
(c) looking at the polychoric one makes me realise yet again that I wish I 
knew more mathematics. I would also find it difficult to test it as I do 
not have any worked examples. Does anyone have any tips about how to 
program it and how to test the resultant code?
(d) I appreciate this last item is not strictly an R question, but my 
intention is to use these as input into the sem package for structural 
equation models. If anyone thinks that is misguided I would be intersted to 
here.


Michael Dewey
m.dewey at iop.kcl.ac.uk

Dear Michael,

I'm not aware of pre-existing R code for tetrachoric or polychoric
correlations. I may at some point incorporate such functions into the sem
package but I don't have concrete plans for doing so. On the other hand, I
don't think that it would be very hard to do so. (A discussion, references,
and an example are in Kotz and Johnson, eds., Encyclopedia of Statistics,
Vol 7.)

Tetrachoric and polychoric correlations are estimates, and in subsequently
estimating a SEM from these, one should take that into account. 

Regards,
 John

--------------------------------
John Fox
Department of Sociology
McMaster University
Hamilton, Ontario
Canada L8S 4M4
905-525-9140x23604
http://socserv.mcmaster.ca/jfox 
-------------------------------- 
> -----Original Message-----
> From: r-help-bounces at stat.math.ethz.ch 
> [mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of Michael Dewey
> Sent: Sunday, November 28, 2004 10:28 AM
> To: r-help-stat.math.ethz.ch
> Subject: [R] Tetrachoric and polychoric ceofficients (for 
> sem) - any tips?
> 
> About two years ago there was a thread about this which 
> suggested that at that time nobody had these coefficients ready to go.
> (a) has anyone in the meanwhile programmed them?
> (b) I think I can see how to do the tetrachoric one with 
> mvtnorm on similar lines to an example on the help page so 
> will try that if nobody else already has
> (c) looking at the polychoric one makes me realise yet again 
> that I wish I knew more mathematics. I would also find it 
> difficult to test it as I do not have any worked examples. 
> Does anyone have any tips about how to program it and how to 
> test the resultant code?
> (d) I appreciate this last item is not strictly an R 
> question, but my intention is to use these as input into the 
> sem package for structural equation models. If anyone thinks 
> that is misguided I would be intersted to here.
> 
> 
> Michael Dewey
> m.dewey at iop.kcl.ac.uk
> 
> ______________________________________________
> R-help at stat.math.ethz.ch mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide! 
> http://www.R-project.org/posting-guide.html

Dear Michael,

I had some time this evening, so I programmed the two-step procedure
described in the article that I mentioned. This isn't the ML estimate of the
correlation, but apparently it performs reasonably well and it is quite
fast. I checked the function on some examples and it appears to work
correctly. I'd be curious to see how the this function compares with the one
that you received.

A more complete solution would take a data frame and, as appropriate,
calculate polychoric, polyserial, and product-moment correlations among its
columns. I don't think that writing a polyserial-correlation function would
be any more difficult. Perhaps I'll add this to the sem package; I hesitate
to do so because the resulting standard errors and likelihoods from sem()
won't be right.

I'm taking the liberty of copying this reply to the r-help list, since the
question was originally raised there. I hope that's OK.

Regards,
 John 


-------------- snip ------------

polychor <- function (x, y){
# x: a contingency table of counts or an ordered categorical variable
# y: if x is a variable, a second ordered categorical variable
# returns the polychoric correlation for the table
#  or between x and y, using the two-step approximation
#  to the ML estimate described in F. Drasgow, "Polychoric and
#  polyserial correlations," in S. Kotz and N. Johnson, eds.
#  The Encyclopedia of Statistics, Volume 7, New York: Wiley,
#  1986.
  f <- function(rho) {
    P <- matrix(0, r, c)
    R <- matrix(c(1, rho, rho, 1), 2, 2)
    for (i in 1:r){
      for (j in 1:c){
        P[i,j] <- pmvnorm(lower=c(row.cuts[i], col.cuts[j]),
                          upper=c(row.cuts[i+1], col.cuts[j+1]),
                          corr=R)
        }
      }
     - sum(tab * log(P))
    }
  tab <- if (missing(y)) x else table(x, y)
  r <- nrow(tab)
  c <- ncol(tab)
  n <- sum(tab)
  row.cuts <- c(-Inf, qnorm(cumsum(rowSums(tab))/n))
  col.cuts <- c(-Inf, qnorm(cumsum(colSums(tab))/n))
  optimise(f, interval=c(0, 1))$minimum
  }

> -----Original Message-----
> From: Michael Dewey [mailto:m.dewey at iop.kcl.ac.uk] 
> Sent: Monday, November 29, 2004 1:38 PM
> To: John Fox
> Subject: RE: [R] Tetrachoric and polychoric ceofficients (for 
> sem) - any tips?
> 
> At 18:07 28/11/04, you wrote:
> >Dear Michael,
> >
> >I'm not aware of pre-existing R code for tetrachoric or polychoric 
> >correlations. I may at some point incorporate such functions 
> into the 
> >sem package but I don't have concrete plans for doing so. On 
> the other 
> >hand, I don't think that it would be very hard to do so. (A 
> discussion, 
> >references, and an example are in Kotz and Johnson, eds., 
> Encyclopedia 
> >of Statistics, Vol 7.)
> 
> Someone has kindly emailed me some code for the polychoric 
> case (which he says is quite slow) I will try it out, it may 
> be better to treat the 2 by 2 case separately. If it is OK I 
> plan to write an equivalent to cor for matrices of 
> tetrachoric/polychoric. It will not happen any time soon now, 
> but if I do manage t would you be interested in it for sem? 
> As you say there remains the problem that they are estimates 
> and introduce further uncertainties.
> 
> 
> >Tetrachoric and polychoric correlations are estimates, and in 
> >subsequently estimating a SEM from these, one should take 
> that into account.
> 
> Michael Dewey
> m.dewey at iop.kcl.ac.uk
>