Manually Calculating Odds from POLR Model

From: "John Fox" <jfox at mcmaster.ca>
To: "'Tate Avery'" <tate_sterling_avery at hotmail.com>
CC: <r-help at stat.math.ethz.ch>
Subject: RE: [R] Manually Calculating Odds from POLR Model
Date: Fri, 12 Aug 2005 19:22:23 -0400

Dear Tate,

If I understand correctly what you're asking, the formulas are on p. 21 of
the paper at
<http://socserv.socsci.mcmaster.ca/jfox/Papers/logit-effect-displays.pdf>.
But why do you want to do this when you can get the fitted probabilities
from predict()?

I hope this helps.
 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 Tate Avery
Sent: Friday, August 12, 2005 2:50 PM
To: r-help at stat.math.ethz.ch
Subject: [R] Manually Calculating Odds from POLR Model

Hello,

I am using polr(...) to generate a model.  The summary shows
the coefficients and the intercepts.

For example:

    coefficient for x1 = c1
    coefficient for x2 = c2

    intercept A|B = i1
    intercept B|C = i2

I can then run predict(..., type="p") with the model and see
the odds for each factor.

For example:

      A        B        C
1    0.3     0.5      0.2
2    0.4     0.1      0.5

What I really want to be able to do is take the 2
coefficients, the 2 intercepts, the x1 & x2 values and
manually calculate the probabilities generated by predict().

I have been searching quite extensively for the underlying
calculations that transform the polr output and the input
variables into the final output odds.  I have tried a number
of dead-end roads so far.

So, if anyone has any information on how to do this or where
I can find out, I would be extremely grateful.

Thank you for your time,
Tate Avery