[R-sig-ME] Can interaction term cause Estimates and Std. Errors to be too large?
ken at kjbeath.com.au
Mon Mar 30 12:50:53 CEST 2009
On 30/03/2009, at 9:21 PM, Jarrod Hadfield wrote:
> Hi Ken,
> Thanks for the reference, it looks interesting. I disagree that
> Luciano's second model should be classified as over fitting. Imagine
> y<-rbinom(100, 1, c(0.001, 0.999))
> summary(glm(y~1, family="binomial"))
> summary(glm(y~x, family="binomial"))
> There is a very high probability of complete separation, the second
> model gives non-significant p-values for the effect of x, but I
> think it would be a mistake to say the 2nd model is over-fitted and
> should be avoided.
My original posting said "usually" and obviously you can create data
with perfect or almost perfect correlation over a large table, but in
practice it commonly happens because there is a small table. One good
reason for producing some descriptive tables before fitting.
> On 30 Mar 2009, at 11:08, Ken Beath wrote:
>> 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.
>> On 30/03/2009, at 7:48 PM, Jarrod Hadfield wrote:
>>> 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.
>>> The University of Edinburgh is a charitable body, registered in
>>> Scotland, with registration number SC005336.
> The University of Edinburgh is a charitable body, registered in
> Scotland, with registration number SC005336.
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