[R-sig-ME] Can interaction term cause Estimates and Std. Errors to be too large?
Ken Beath
ken at kjbeath.com.au
Mon Mar 30 12:08:58 CEST 2009
I meant overfitting in the sense of trying to fit too complex a model,
which is the same as what you are describing. Gelman has some papers
on the use of priors, one is http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.aoas/1231424214
In the case of complete separation the results seem to be very
dependent on the prior which doesn't look to be a good thing. It would
appear much better to admit that there is insufficient data to perform
the analysis.
Ken
On 30/03/2009, at 7:48 PM, Jarrod Hadfield wrote:
> Hi,
>
> I think it unlikely that the problem arises through overfitting in
> the sense that there are too many parameters for the amount of
> data. It's more likely that the underlying probabilities really are
> extreme for some categories causing what are also known as "extreme
> category problems" (eg Miztal 1998 J. Dairy Science 72 1557-1568):
> the binary variable in one or more groups is always 0 or 1, even
> though there are probably many eggs in most categories. A solution
> to this type of problem is to place an informative prior on the
> fixed effects to stop them wandering into extreme values on the
> logit scale. For the purist this may be anathema, but as a practical
> solution it seems to work quite well. Having a normal prior on the
> logit scale with mean zero and variance pi, is the closest (I
> think?) to a uniform prior on the probability scale. If there are
> more elegant solutions to the problem I'd be interested to hear
> about them.
>
> Cheers,
>
> Jarrod
>
>
>
> --
> The University of Edinburgh is a charitable body, registered in
> Scotland, with registration number SC005336.
>
>
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