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Ordinal Mantel-Haenszel type inference

I suspect that what you need will be in "S-PLUS (and R) Manual to  
Accompany Agresti?s Categorical Data Analysis (2002)" 2nd edition by  
Laura A. Thompson, 2007 which I have always been able to find with a  
Google search. Yep, it's still there:

https://home.comcast.net/~lthompson221/Splusdiscrete2.pdf

Its Chapter 7, "Logit Models for Multinomial Responses " discusses  
various cumulative logit models.

The polr function (proportional odds logistic regression) in MASS will  
return the regression equivalent of what you are asking for. Thompson  
says the lrm in the "Desing library" will also do it, by which she  
really means that the lrm in the Design package by Harrell will do it.  
The link she offers is outdated and it doesn't really matter for  
obtaining the Hmisc/Design packages, since they are on CRAN, but  
online available documentation is currently at:

http://biostat.mc.vanderbilt.edu/twiki/bin/view/Main/StatComp

She then also mentions "lcr (library ordinal), and nordr (library  
gnlm)". Later in the chapter she illustrates the use of the vglm  
function in in the vgam package.