[R-sig-ME] calculation of AIC

[John Maindonald]

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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