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

From   Maarten buis <>
Subject   Re: st: interpreting negative and positive AIC- OLS VS. GLM
Date   Thu, 19 Aug 2010 15:38:02 +0000 (GMT)

--- 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, 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 L. Buis
Institut fuer Soziologie
Universitaet Tuebingen
Wilhelmstrasse 36
72074 Tuebingen


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