R help - May 2007 - OT: Predicted probabilities from ordinal regressions

Sorry if this is too off-topic, as we may not implement this in R 
(although we may do so).

A student of mine is looking at some public opinion data in which there 
appears to be a statistically significant difference between levels of 
support for a proposal based on which of two question wordings is used. 
That is, roughly half the sample was asked the question with wording 1, 
the other half with wording 2, and the difference is large enough to be of 
interest (approx. 6 percentage points different with an N of about 
30,000).

The question is how best to model this. In the past I have generated 
predicted probabilities based on the sample asked wording 1, used these to 
assign those asked wording 2 to predicted categories, and used a logistic 
regression to predict difference between predicted and actual response. In 
this case, though, the question of interest uses a four-level ordinal 
response, so ordinary predicted probabilities based on, e.g., and ordinal 
logistic regression generate literally probabilities of being in each of 
the four categories. Transforming this outcome into a prediction of 
membership in one of the given categories is not straightforward. Can 
anyone provide some insight into how to model predicted vs. actual 
outcomes on an ordinal scale?

Thanks.

----------------------------------------------------------------------
Andrew J Perrin - andrew_perrin (at) unc.edu - http://perrin.socsci.unc.edu
Assistant Professor of Sociology; Book Review Editor, _Social Forces_
University of North Carolina - CB#3210, Chapel Hill, NC 27599-3210 USA
New Book: http://www.press.uchicago.edu/cgi-bin/hfs.cgi/00/178592.ctl

Andrew Perrin wrote:
> Sorry if this is too off-topic, as we may not implement this in R 
> (although we may do so).
> 
> A student of mine is looking at some public opinion data in which there 
> appears to be a statistically significant difference between levels of 
> support for a proposal based on which of two question wordings is used. 
> That is, roughly half the sample was asked the question with wording 1, 
> the other half with wording 2, and the difference is large enough to be of 
> interest (approx. 6 percentage points different with an N of about 
> 30,000).
> 
> The question is how best to model this. In the past I have generated 
> predicted probabilities based on the sample asked wording 1, used these to 
> assign those asked wording 2 to predicted categories, and used a logistic 
> regression to predict difference between predicted and actual response. In 
> this case, though, the question of interest uses a four-level ordinal 
> response, so ordinary predicted probabilities based on, e.g., and ordinal 
> logistic regression generate literally probabilities of being in each of 
> the four categories. Transforming this outcome into a prediction of 
> membership in one of the given categories is not straightforward. Can 
> anyone provide some insight into how to model predicted vs. actual 
> outcomes on an ordinal scale?
> 
> Thanks.
With the lrm function in the Design package you can get predicted 
probabilities for each class as well as predicted mean scores.

Frank
> 
> ----------------------------------------------------------------------
> Andrew J Perrin - andrew_perrin (at) unc.edu - http://perrin.socsci.unc.edu
> Assistant Professor of Sociology; Book Review Editor, _Social Forces_
> University of North Carolina - CB#3210, Chapel Hill, NC 27599-3210 USA
> New Book: http://www.press.uchicago.edu/cgi-bin/hfs.cgi/00/178592.ctl
> 
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> 

-- 
Frank E Harrell Jr   Professor and Chair           School of Medicine
                      Department of Biostatistics   Vanderbilt University