calculation of AIC

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