[R-sig-ME] calculation of AIC

[Murray Jorgensen]

Although if log-likelihood is arbitrary up to an additive constant we 
may add a sufficiently large constant onto any two AICs and push the 
first non-equal digit of the two AICs as far down as we want!

Murray Jorgensen

John Maindonald wrote:
> On 02/02/2009, at 11:06 AM, Jeremiah Rounds wrote:
> 
>>
>>> Date: Sun, 1 Feb 2009 11:41:44 -0800> From: adik at ilovebacon.org> To: 
>>> orzack at freshpond.org> CC: r-sig-mixed-models at r-project.org> Subject: 
>>> Re: [R-sig-ME] calculation of AIC> > > On Sun, 1 Feb 2009, orzack 
>>> wrote:> > > Speaking of this, does anybody know how to change the 
>>> default rounding for > > glm (and lmer) OR for an R session in 
>>> general (e.g., so that a regular call > > to glm would generate AIC 
>>> values with more digits)?> > > 1/7> [1] 0.1428571> > 
>>> options(digits=22)> > 1/7> [1] 0.1428571428571428> > 
>>> options(digits=23)> Error in options(digits = 23) :> invalid 'digits' 
>>> parameter, allowed 1...22> > options(digits=22)> > ...but this of 
>>> course won't help if there is explicit rounding programmed> into 
>>> glm/lmer. I also do not understand what would motivate this code,> 
>>> instead of a more straightforward round(aic,0).> > --Adam
>>
>> First, glm apparently is not using rounding from "round".  glm is 
>> using signif or equivalent logic.  There is a difference. The 
>> difference is significant digits is a fairly precisely defined 
>> notion.  It is the number of digits you keep on the front of the power 
>> of 10 in "a X 10^b".  Round is much more cosmetic from what I can tell.
>>
>> Second,  round(aic,0) is not more straightforward in the presence of 
>> very small AIC.  Here the distinct difference from round(a,0) and 
>> signif(a,4) is that you never know prior to viewing the aic how many 
>> digits round(a,0) will be keeping from the original unrounded AIC 
>> value.  With signif(a,4) you always know there will be a 4 digit 
>> number times 10 to some power.
>>
>> Third, in my limited statistical experience (I am a master's student) 
>> AIC is not a method where those extra digits ever really matter.  I 
>> did a project on AIC/BIC model selection.  IMO in order to use AIC 
>> properly you have to consider the models in a nearby neighborhood to 
>> the best AIC as just as good as the model with the best AIC and 
>> consider sensitivity in your estimates.    There is no real context 
>> where you can properly say "the fifth significant digit of AIC has 
>> decided that model A is better than model B, and so I discard model B."
> 
> Well said!
> 
> John Maindonald             email: john.maindonald at anu.edu.au
> phone : +61 2 (6125)3473    fax  : +61 2(6125)5549
> Centre for Mathematics & Its Applications, Room 1194,
> John Dedman Mathematical Sciences Building (Building 27)
> Australian National University, Canberra ACT 0200.
> 
>> That is what I think,
>> Jeremiah
>>
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-- 
Dr Murray Jorgensen      http://www.stats.waikato.ac.nz/Staff/maj.html
Department of Statistics, University of Waikato, Hamilton, New Zealand
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