[R-sig-ME] Can interaction term cause Estimates and Std. Errors to be too large?

[Ken Beath]

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
>
>
>
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