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Re: st: Opinions on fractional logit versus tobit - prediction and model fit


From   Eva Poen <eva.poen@gmail.com>
To   Statalist <statalist@hsphsun2.harvard.edu>
Subject   Re: st: Opinions on fractional logit versus tobit - prediction and model fit
Date   Fri, 3 Apr 2009 22:00:58 +0100

<>

Mike,

many thanks for your comments, and the extensive list of references.
Much appreciated.

2009/4/2  <carlto12@msu.edu>:
> With a significant portion of the data piled up at these values it
> may make sense to use a two limit tobit model.

The jury is still out on this one, judging from the responses. Am I
right in gathering that, although both models are probably
misspecified, the glm version is more robust against misspecification
and therefore worth pursuing?

> While it is true that the
> fractional models proposed by Papke and Wooldridge (1996, 2008) {2008
> Journal of econometrics: they extend the fractional response models to a
> panel data setting} are quasi-likelihood does not mean that the predicted
> values are not valuable. As long as you have correctly specified the
> conditional mean function this implies that you have consistent, although
> inefficient estimates.

OK, thanks, I was starting to get confused with what I can validly
interpet with this approach.

> If your interest is in Average Partial Effects (APEs)
> then the fractional response models will allow you to get consistent
> estimates of these, regardless of the variance structure.

While I am certainly interested in average partial effects, one of the
main points of doing this is to learn more about the heterogeneity,
and therefore the random effects themselves. I might end up doing some
simulations, in order to asses the estimates that -gllamm- delivers.
However, given that a single run on 2000 observations can take many
hours to converge, this could be a very lengthy exercise...

Thanks again,
Eva

>
> Hope this helps,
> Mike
>
> References:
>
> Gourieroux, C., A. Monfort and A. Trognon (1984), ?Pseudo Maximum Likelihood
> Methods: Theory,? Econometrica, 52, pp. 681-700.
> Papke, L. and J. M. Wooldridge (1996), ?Econometric Methods for Fractional
> Response Variables with an Application to 401(k) Plan Participation Rates,?
> Journal of Applied Econometrics, 11, pp. 619-632.
> Papke, L. and J. M. Wooldridge (2008), ?Panel Data Methods for Fractional
> Response Variables with an Application to Test Pass Rates,? Journal of
> Econometrics, 145, pp. 121-133
> Chamberlain, G (1984), "Panel Data", Handbook of Econometrics. (Also on NBER
> I think)
>
>
>
> Quoting "Eva Poen" <eva.poen@gmail.com>:
>
>> <>
>>
>> I'm looking at different ways to model my outcome variable, which is
>> bounded between zero and one (zero and 20, actually, but I don't mind
>> modelling the fraction). It's panel data, and I would like to model
>> individual heterogeneity in the form of random effects (both random
>> intercepts and random slopes). There are a lot of observations at zero
>> and one, respectively. I'm reasonably confident that the random
>> effects are independent of the other variables in the model.
>>
>> So far I have been looking at the fractional logit model, as
>> introduced by Papke and Wooldrigde in their 1996 Journal of Applied
>> Econometrics paper. I use -gllamm- to estimate a model with random
>> effects. I have also been looking at the tobit model, which I again
>> estimate using -gllamm- with random effects.
>>
>> I have a few doubts about the fractional logit model (FLM), and would
>> like to hear other people's opinion:
>>
>> - Although it appears to be a very elegant solution, some people say
>> that FLM is not well suited for problems with a lot of zeros or ones;
>> for example, Maarten Buis said so in this post (but didn't provide a
>> reference): http://www.stata.com/statalist/archive/2007-07/msg00786.html
>> If someone knows any references where this is discussed, I'd be
>> grateful to receive them.
>>
>> - Since FLM is quasi-likelihood, any likelihood-based approaches to
>> model fit are ruled out. For the tobit model I can use those measures.
>> The only other option I can think of for FLM is to compare predicted
>> values with actual values. However, do predicted values in FLM make
>> sense? We know that the distributional assumption is not true. So I'm
>> wondering how meaningful predicted values are in this context.
>>
>> - I am getting sensible estimates for the random effects with the
>> tobit approach, and not so sensible ones with FLM. In fact, FLM
>> estimates two of the three to be zero. Is this a sign of my model
>> being incorrectly specified, or could it be a sign of FLM not handling
>> the zeros and ones very well?
>>
>> Many thanks,
>> Eva

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