[ADMB Users] mildly robust methods in count models

[dave fournier]

>  Where I disagree mildly is that in looking at **this particular case**
>it seems to me that there are not important qualitative differences
>between the fits.  Yes, the type I error rate/coverage is definitely
>better with the robust model (5.4% vs 7.7% of the time).  In my own
>personal universe, 50% undercoverage (i.e. approx 7.5% type I error rate
>for a nominal rate of 5%) is fairly bad, but not terrible -- in the
>context of all the other things that are always wrong with the model
>that we can't control, I consider that a moderate but not an
>earth-shattering problem.

Well it just happened to be the first example I could run easily.

Just to finish it off I thought I would compare the robust and nonrobust
type 2 (I think you call it) fit to the data, i.e. Mollie's original
model.  Again I added a covariance consisting of N(0,1) random noise.
I increased the number of simulations to 40,000 to try and make it
bulletproof.

For the robust model
> sum(as.numeric(x>3.84))/length(x)
[1] 0.0566

For the original model
> sum(as.numeric(y>3.84))/length(y)
[1] 0.0325

That came as a complete surprise to me.
So the original model formulations only rejects the null hypothesis 3.25% of the time.
That seems pretty bad.

The robut procedure improves on both model formulations.  So robustness is robust.


> Robust methods are definitely on the list,
>but they might fall below (e.g.) getting people to stop using stepwise
>approaches ...


I can hear this conversation where someone is saying, I will agree to
use (mildly)robust methods, but only of you let me use a stepwise approach.