[ADMB Users] mildly robust methods in count models

[dave fournier]

On 12-12-14 09:04 AM, H. Skaug wrote:

I think that there are a number of issues. Two that come to mind are

First is to verify my claim for each type of example
that these methods perform nearly as well as the nonrobust methods when the
null hypothesis is satisfied.  This would  show that there is 
(virtually) no risk in using them.

Another issue is to investigate real examples to see how often one gets 
different
results for various estimates and tests.  It would be nice to use the 
glmmadmb framework
if possible.  So long as glmmadmb can create the correct dat and pin 
files it is simple
to modify the glmmadmb.tpl to do the robust estimates.  This should 
enable us to
use a lot of data sets that are available in R.  I quess that R users 
would also find the results
more accessible conceptually.



> 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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