[R-sig-ME] model selection in lme4

[Ben Bolker]

Took a (very) quick look at Raftery, which all seems sensible
and well-argued.  However ... the paper contrasts Bayes/BIC
with classical hypothesis testing.  Many of the points listed on p. 155
(better assessment of evidence, applicability to non-nested models, take
model uncertainty into account, allow model averaging, easy to
implement) apply to AIC as well as BIC.  BIC does have many good
qualities (approximation to Bayes factor, sensible "flat prior"
interpretation, statistical consistency, ...).  But the crux of the
argument between BIC and AIC is the difference in their objective. BIC
aims to identify the "true model", which essentially assumes that there
is a sharp cutoff between parameters/processes that are in the model and
those that are out. Burnham and Anderson have a lot to say about
tapering effect sizes; they are zealots about AIC, and I often discount
their enthusiasm, but after much percolation I've decided that AIC
really does make sense for the kinds of questions I (and many
ecologists) tend to ask.

   When you say that AIC selects an overly complex model, how
do you know what the correct model is and which parameters are
unnecessary?  Is this a case of fitting to simulation output?
In that case I might bring up B&A's "tapering effects" argument
again -- selecting the correct model with a fixed number of parameters
with non-tapering effects is what BIC is for, not what AIC is for.

  I have tried to say this more coherently at
http://emdbolker.wikidot.com/blog:aic-vs-bic

  As an aside, I don't have a vested interest in this, and I don't
claim that AIC is better for everything ... just that it seems
most ecologists are working with "true models" that are of
arbitrarily large dimension with tapering effects, which is where
AIC should select the model with the best predictive capability ...

  Ben Bolker

Christopher David Desjardins wrote:
> For a discussion of BIC, please see Raftery (1995) in Sociological 
> Methodology. Before you commit yourself on the AIC, I do encourage you to 
> look at your BIC. In the models I've run when there is disagreement between 
> the BIC and the AIC, it's usually that the AIC selects the overly complex 
> model and includes unnecessary parameters.
> Cheers,
> Chris
> 
> On Sunday 15 February 2009 19:50:30 Ben Bolker wrote:
>>   It would be better to use AICc, but I'm not sure what I would
>> use for "number of parameters" for a random effect with n
>> levels: any number between 0.5 and n seems plausible!
>> Someone should send Shane Richards (who has done some
>> very nice work testing (Q)AIC(c) in ecological settings)
>> and see if he's willing to tackle this one, although I can
>> imagine he's getting sick of this kind of exercise ...
>>
>>   Ben Bolker
>>
>> Renwick, A. R. wrote:
>>> Just a quickie Ben,
>>> Are you saying that you would use AIC rather than AICc even with
>>> small sample size - due to difficulty in counting residual degrees of
>> freedom?
>>
>>> Thanks
>>> Anna
>>> p.s. this forum really is fantastic
>>>
>>> ________________________________________
>>> From: r-sig-mixed-models-bounces at r-project.org
>>> [r-sig-mixed-models-bounces at r-project.org] On Behalf Of Ben Bolker
>>> [bolker at ufl.edu] Sent: 15 February 2009 23:07
>>> To: Christopher David Desjardins
>>> Cc: r-sig-mixed-models at r-project.org; tahirajamil at yahoo.com
>>> Subject: Re: [R-sig-ME] model selection in lme4
>>>
>>>   Some caution on this advice: you seem to be quoting
>>> the general advice on AIC/BIC/AICc
>>>
>>>   1. The AIC/BIC distinction is between "best prediction"
>>> and "consistent estimation of true model" dimension, e.g.
>>>
>>> Yang, Yuhong. 2005. Can the strengths of AIC and BIC be shared? A
>>> conflict between model identification and regression estimation.
>>> Biometrika 92, no. 4 (December 1): 937-950. doi:10.1093/biomet/92.4.937.
>>>
>>>   I favor AIC on these grounds, but you can decide for yourself.
>>>
>>>   2. For models with different random effects, AIC and BIC share
>>> a "degrees of freedom counting" problem with all model selection
>>> approaches -- there are two aspects here, (1) whether you are
>>> focused on individual-level prediction or population-level
>>> prediction (Vaida and Blanchard 2005, Spiegelhalter et al 2002)
>>> and (2) whether AIC/BIC share the boundary problems that
>>> also apply to likelihood ratio tests (Greven, Sonja. 2008. Non-Standard
>>> Problems in Inference for Additive and Linear Mixed Models. Göttingen,
>>> Germany: Cuvillier Verlag.
>>> http://www.cuvillier.de/flycms/en/html/30/-UickI3zKPS,3cEY=/Buchdetails.h
>>> tml?SID=wVZnpL8f0fbc. )
>>>
>>>   3. AIC and BIC are asymptotic tests (which can be especially
>>> problematic with random effects problems, when there are not
>>> large number of random blocks -- this makes likelihood ratio
>>> tests NOT OK for fixed-effect comparisons with small numbers
>>> of blocks (Pinheiro and Bates 2000)).  If you want to use
>>> AICc then you are back to counting residual degrees of freedom ...
>>> as far as I know there isn't much guidance available on this
>>> issue.
>>>
>>>   My bottom line:
>>>
>>>   I would go ahead and use (Q)AIC with caution for data sets with large
>>> (?) numbers of blocks.  With smaller numbers of blocks I would probably
>>> try to find some kind of randomization/permutation approach to get a
>>> sense of the relevant size of delta-AIC values ...
>>>    ... or damn the torpedoes and see if you can get away with straight
>>> AIC.
>>>
>>>   Ben Bolker
>>>
>>> Christopher David Desjardins wrote:
>>>> You could use either the BIC or the AIC. My understanding is that the
>>>> AIC tends to favor overly complex models whereas the BIC tends to
>>>> favor parsimonious models. I am generally inclined to always use the
>>>> BIC. If you have a small sample size you might also consider using the
>>>> AICC which is a correction of the AIC for small sample sizes. That
>>>> said, in my experience the AICC still selects more complex models than
>>>> the BIC. Also if you have nested models you could use the chi-square
>>>> tests.
>>>> Cheers,
>>>> Chris
>>>>
>>>> On Feb 15, 2009, at 4:44 PM, Tahira Jamil wrote:
>>>>> Hi
>>>>> I have run  GLMM models in lme4 with different fixed effects and
>>>>> random effects . But now the problem is model selction Is AIC or BIC
>>>>> results are definitive specially for Gernalized linear mixed models
>>>>> or what critera should I use for model selction. So I can decide
>>>>> which explantory variable should be in the model because I have more
>>>>> than 10 explantory variables and some are entering in the model as
>>>>> random effect. In some cases If AIC has lower value but BIC is
>>>>> comparatively high.
>>>>>    some suggestion for model selection would be highly appricated.
>>>>>
>>>>>    WIth best wishes
>>>>>    T Jamil
>>>>>    Ph.D student
>>>>>    Biometris
>>>>>    Wageningen University and Research centre Netherlands.
>>>>>
>>>>> _______________________________________________
>>>>> R-sig-mixed-models at r-project.org mailing list
>>>>> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
>>>> -----------------
>>>> Christopher David Desjardins
>>>> Ph.D. Student
>>>> Quantitative Methods in Education
>>>> Department of Educational Psychology
>>>> University of  Minnesota
>>>> http://blog.lib.umn.edu/desja004/educationalpsychology/
>>>>
>>>> _______________________________________________
>>>> R-sig-mixed-models at r-project.org mailing list
>>>> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
>>> --
>>> Ben Bolker
>>> Associate professor, Biology Dep't, Univ. of Florida
>>> bolker at ufl.edu / www.zoology.ufl.edu/bolker
>>> GPG key: www.zoology.ufl.edu/bolker/benbolker-publickey.asc
>>>
>>> _______________________________________________
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>>> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
>>>
>>>
>>> The University of Aberdeen is a charity registered in Scotland, No
>>> SC013683.
> 
> 


-- 
Ben Bolker
Associate professor, Biology Dep't, Univ. of Florida
bolker at ufl.edu / www.zoology.ufl.edu/bolker
GPG key: www.zoology.ufl.edu/bolker/benbolker-publickey.asc