[R] Follow-up about ordinal logit with mixtures: how about 'continuation ratio' strategy?

[Paul Johnson]

On 5/10/07, Frank E Harrell Jr <f.harrell at vanderbilt.edu> wrote:
> Paul Johnson wrote:
> > This is a follow up to the message I posted 3 days ago about how to
> > estimate mixed ordinal logit models.  I hope you don't mind that I am
> > just pasting in the code and comments from an R file for your
> > feedback.  Actual estimates are at the end of the post.
>
> . . .
>
> Paul,
>
> lrm does not give an incorrect sign on the intercepts.  Just look at how
> it states the model in terms of Prob(Y>=j) so that its coefficients are
> consistent with the way people state binary models.
>
> I'm not clear on your generation of simulated data.  I specify the
> population logit, anti-logit that, and generate binary responses with
> those probabilities.  I don't use rlogis.

Thank you.

I don't think I'm telling you anything you don't already know, but for
the record, here goes.  I think the difference in signs is just
convention within fields.  In choice models (the econometric
tradition), we usually write that the response is in a higher category
if

eta + random > cutpoint

and that's how I created the data--rlogis supplies the random noise.  Then

eta - cutpoint > random

or

cutpoint - eta < random

and so

Prob ( higher outcome ) = Prob ( random > cutpoint - eta)

In the docs on polr from MASS, V&R say they have the logit equal to

cutpoint - eta

so their parameterization is consistent with mine.  On the other hand,
your approach is to say the response is in a higher category if

 intercept + eta > random,

where I think your intercept is -cutpoint. So the signs in your
results are reversed.

-cutpoint + eta > random


But this is aside from the major question I am asking.  Do we think
that the augmented data frame approach described in Cole, Allison, and
Ananth is a good alternative to maximum likelihood estimation of
ordinal logit models, whether they are interpreted as proportional
odds, continuation, or stopping models?   In the cases I've tested,
the parameter estimates from the augmented data frame are consistent
with polr or lrm, but the standard errors and other diagnostic
informations are quite different.

I do not think I can follow your suggestion to use penalties in lrm
because I have to allow for the possibilities that there are random
effects across clusters of observations, possibly including random
slope effects, but certainly including random intercepts for 2 levels
of groupings (in the HLM sense of these things).

Meanwhile, I'm studying how to use optim and numeric integration to
see if the results are comparable.

pj

> See if using the PO model with lrm with penalization on the factor does
> what you need.
>
> lrm is not set up to omit an intercept with the -1 notation.
>
> My book goes into details about the continuation ratio model.
>
> Frank Harrell
>





-- 
Paul E. Johnson
Professor, Political Science
1541 Lilac Lane, Room 504
University of Kansas