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

[Jarrod Hadfield]

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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