Re: st: interpreting negative and positive AIC- OLS VS. GLM

[Arina Viseth <arina@UDel.Edu>]

Thank you very much Maarten for your answer. It is very helpful.

Arina

---- Original message ----
>Date: Thu, 19 Aug 2010 15:38:02 +0000 (GMT)
>From: owner-statalist@hsphsun2.harvard.edu (on behalf of Maarten buis <maartenbuis@yahoo.co.uk>)
>Subject: Re: st: interpreting negative and positive AIC- OLS VS. GLM  
>To: statalist@hsphsun2.harvard.edu
>
>--- On Thu, 19/8/10, Arina Viseth wrote:
>> I am trying to run a regression on unemployment rates, I
>> compare OLS output with fractional logit estmates (since the
>> unemployment rate is bounded between zero and one). To
>> assess goodness of fit of the models, I get AIC (OLS) is
>> negative 1004 while AIC (glm)*number of observations is
>> positive 169.
>
>Within OLS you will (almost) always get negative AICs when
>your dependent variable ranges between 0 and 1. This is 
>because the likelihood will (almost) always be larger than
>1 (We fit a bell shaped curve to a range between 0 and 1,
>with the constraint that the area under the curve equals
>1, so the maximum density will almost always be larger than
>1.) Take the log of a number larger than 1, and you will get
>a positive number, transform that to a AIC or BIC, and they
>will be negative.
>
>If we change our depenent variable to refer to percentages
>rather than proportions (just multiply your dependent 
>variable by 100), then we are not realy changing the model.
>However, now the AIC will almost certainly be negative.
>
>below is an example that shows this behaviour.
>
>*------------------ begin example ------------------
>use http://fmwww.bc.edu/repec/bocode/c/citybudget.dta, clear
>reg governing minorityleft noleft houseval popdens
>estat ic
>
>replace governing = governing * 100
>reg governing minorityleft noleft houseval popdens
>estat ic
>*------------------- end example -------------------
>
>I would feel very uncomfortable with choosing a model in
>such a way that is fully determined by the arbitray choice
>whether we model proportions or percentages.
>
>Hope this helps,
>Maarten
>
>--------------------------
>Maarten L. Buis
>Institut fuer Soziologie
>Universitaet Tuebingen
>Wilhelmstrasse 36
>72074 Tuebingen
>Germany
>
>http://www.maartenbuis.nl
>--------------------------
>
>
>      
>
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