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From | Maarten buis <maartenbuis@yahoo.co.uk> |
To | statalist@hsphsun2.harvard.edu |
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 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 -------------------------- * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/