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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   st: Opinions on fractional logit versus tobit - prediction and model fit
Date   Thu, 2 Apr 2009 19:27:39 +0100

<>

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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