[ADMB Users] mildly robust methods in count models

[H. Skaug]

Hi,

I agree fully with you about the need for robust methods and that ADMB
is a great
tool for implementing such. However, and "robustification" is a generic
tool and should be documented separately from other modelling issues.
I think we need a document (with small  tpl examples), written in a
pedagogical way,
describing  how all the standard probability distributions should
be robustified. That would be a good resource for people who want to
learn about robust methods.

If somebody is willing to develop such a suite I will upload it immediately as
an example on the webpage, but currently I am not able to develop this
from scratch  myself.

Hans

On Fri, Dec 14, 2012 at 5:09 PM, dave fournier <davef at otter-rsch.com> wrote:
> 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
>
>
>
>
>
>
>
>
>
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