Date:         Fri, 4 Jul 2003 11:25:22 +0300
Reply-To:     Akin Pala <akin@DR.COM>
Sender:       "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
From:         Akin Pala <akin@DR.COM>
Subject:      Re: akaike's in repeated, small or big value?

Well, this explanation:
 When we have negative values for the information criterion then we must
have the first
form (larger is better), while if we have positive values for the criterion
we must have the second form (smaller is better).  In either case, we have
smaller absolute value is better.
is very clear. Thanks!

--
Akin Pala, Ph.D.
http://akin.owns.it
Tel: (286) 218 00 18 ext. 1349
"Dale McLerran" <stringplayer_2@YAHOO.COM> wrote in message
news:20030703175632.89769.qmail@web21102.mail.yahoo.com...
> --- Jay Weedon <jweedon@EARTHLINK.NET> wrote:
> > On Thu, 3 Jul 2003 13:00:59 +0300, "Akin Pala" <akin@dr.com> wrote:
> >
> > >When using repeated statement in proc mixed, should I use the model
> > with
> > >highest AIC, or with highest absolute value of AIC=lowest value
> > since it is
> > >usually negative? This is what it says in sas online manual in a
> > repeated
> > >example:
> > >/*
> > >Both Akaike's Information Criterion (-208.4) and Schwarz's Bayesian
> > >Criterion (-211.0) are larger for this model than for the
> > homogeneous
> > >compound symmetry model (-216.3 and -217.6, respectively). This
> > indicates
> > >that the heterogeneous model is more appropriate.
> > >*/
> > >so, they say use the model with the highest AIC value.
> > >BUT HERE IS WHAT THEY SAY IN SOME OTHER PLACE in sas online manual:
> > >/*
> > >Akaike's Information Criterion (AIC) (Akaike 1974; Akaike 1987)
> > >This is a criterion for selecting the best model among a number of
> > candidate
> > >models. The model that yields the smallest value of AIC is
> > considered the
> > >best.
> > >Consistent Akaike's Information Criterion (CAIC) (Bozdogan 1987)
> > >This is another criterion, similar to AIC, for selecting the best
> > model
> > >among alternatives. The model that yields the smallest value of CAIC
> > is
> > >considered the best. CAIC is preferred by some people to AIC or the
> > test.
> > >Schwarz's Bayesian Criterion (SBC) (Schwarz 1978; Sclove 1987)
> > >This is another criterion, similar to AIC, for selecting the best
> > model. The
> > >model that yields the smallest value of SBC is considered the best.
> > SBC is
> > >preferred by some people to AIC or the  test.
> > >*/
> >
> > I agree that the documentation of proc mixed is both confusing and
> > contradictory on this matter.
> >
> > If you read the documentation of the IC option in the proc mixed
> > statement, you'll see that AIC (and the other criteria) can be
> > expressed in both "larger is better" and "smaller is better" forms.
> >
> > To add to the confustion is the fact that (IIRC) the default output
> > has changed over time, so you should read the definitions of the
> > criteria and check which are being output by the version of SAS
> > you're
> > using. Recent versions of SAS output only "smaller is better"
> > statistics unless IC is specified.
> >
> > Do not disregard the sign of the criterion: -208 is larger than -216,
> > so if you're using a "smaller is better" statistic, the first of
> > these
> > suggests a worse fit.
> >
> > JW
>
> Well said!  I would note that if the sign of the criterion
> is negative, then a larger is better model is being assumed.
> That is because all of the information criteria have a form
> of either ll-q where ll is the log likelihood (necessarily
> negative, with larger is better interpretation) and q is a
> positive penalty function based on the size of the estimated
> model, or a form -2*(ll-q).  When we have negative values
> for the information criterion then we must have the first
> form (larger is better), while if we have positive values
> for the criterion we must have the second form (smaller is
> better).  In either case, we have smaller absolute value
> is better.
>
> Dale
>
>
> =====
> ---------------------------------------
> Dale McLerran
> Fred Hutchinson Cancer Research Center
> mailto: dmclerra@fhcrc.org
> Ph:  (206) 667-2926
> Fax: (206) 667-5977
> ---------------------------------------
>
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