[ADMB Users] mildly robust methods in count models

[dave fournier]

On 12-12-13 08:43 PM, Hans J. Skaug wrote:

Hi,

BTW Hans, I think you misunderstood my remarks about robustness in
count models. I haven't got any response so I am kicking the wasp nest 
again.
  My feeling is that there appear to be two schools,
those who blindly use standard non-robust methods and those
who use very robust methods.  While there may be situations
where very robust methods are a good idea, what I am advocating
is to routinely use mildly robust methods.  My reasoning is that
mildly robust methods perform almost as well as the standard
methods when the non robust hypothesis is satisfied and
they perform much better when just a small amount of
contamination is introduced.   I don't think Ben gets this point.
He notes that the point estimates are nearly the same.  This
is just like the fact that for normal theory estimates of means
are more insensitive to outliers than estimates of variances.
However it is the estimates of variances that are important
for significance tests.

To test out these ideas I took Mollies negative binomial model with the 
fir data and
added a covariate which was random noise.  With the non-robust
model including this covariate  was considered significant 7.7% of
the time while the robust version it was 5.4% of the time, much closer
to the theoretical value of 5%.  Why do I think this is an ADMB thing?

The reason that the R gurus avoid these ideas is that they don't
fit into their simple exponential family methodology.  With ADMB it is
is a trivial extension to the model.

A major problem (and I know I have said this before) with promoting ADMB is
that it always seems that to compare it so say R you have to use methods 
that
R deems to be legitimate.  So these mildly robust methods never come up.
Rather the question is always posed as either standard non-robust methods or
extreme robust methods like Huber stuff.  I think that ADMB can do a 
great service to
the statistical community by making these mildly robust methods more
widely known.

For the record the mildly robust method for the negative binomial with 
parameters mu and tau
where tau>1 is the overdispersion would be to use something like

                   (1-p)*NB(mu,tau)+p*NB(mu,q*tau)

where p and q may be estimated or held fixed.  Typical values for p and 
q are .05 and 9.0.
For mollies fir model these were estimated.

This all came up first when I came across an interesting article on the 
web which
stated (and seemed to demonstrate)
that max like should never be used in NB count models for significance 
tests on the
fixed effects because this lack of robustness led  to rejecting the null 
hypothesis
too often.  They advocated quasi-likelihood or GEE instead.   As a fan 
of max like
I wondered if it could be "fixed" for these models.

  Wish I could find that article again.

            Dave