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

[Frank E Harrell Jr]

Paul Johnson wrote:
> 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

Just want to make sure that samples it generates are from the correct 
probability model.  I'm just used to doing this with ifelse(runif(n) <- 
plogis(population.logit)) for the binary case.

> 
> 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.

Then I wouldn't use the augmented data approach.

> 
> 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).

My suggestion doesn't handle random slopes but does handle random 
intercepts in a sense.

Good luck
Frank

> 
> 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
>>
> 
> 
> 
> 
> 


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