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Manually Calculating Odds from POLR Model

4 messages · Tate Avery, John Fox

Original
Tate Avery
# 
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
John Fox
# 
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 
--------------------------------
2 days later
Tate Avery
# 
John,

Thank you, the document was very helpful.  I can now calculate the same 
values generated by predict() when I am using purely numeric input data.

Another small question arises when I look at the example using 'housing' in 
the polr() documentation page:

Running the example produces the following coefficients...

Coefficients:
   InflMedium      InflHigh TypeApartment    TypeAtrium   TypeTerrace      
ContHigh
    0.5663924     1.2888218    -0.5723552    -0.3661912    -1.0910195     
0.3602834

Now, if I am trying to perform a prediction and the value for INFL comes in 
as 'Medium' what is done?  And, what is done for 'low'?

That seems to be the last missing piece in my understanding of how to 
convert the model values into predictions.

Thank you,
Tate
John Fox
# 
Dear Tate,

Your question pertains generally to the treatment of factors in model
formulas and is not particular to polr(). For a brief explanation, see
Section 11.1, "Defining statistical models; formulae," and in particular
Section 11.1.1 on "Contrasts" in the manual An Introduction to R, which is
distributed with R. More detailed explanations are in texts such as Venables
and Ripley, Modern Applied Statistics With S, and my own, An R and S-PLUS
Companion to Applied Regression. 

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 
--------------------------------
isplays.pdf>.