On Sat, 5 Aug 2006, Andreas Beyerlein wrote:
> Dear all,
>
> I want to compare some different models for a dataset by QQ plots and
> AIC. I get the following AICs:
>
> - linear model: 19759.66
> - GAMLSS model: 18702.7
> - linear model with lognormal response: -7862.182
>
> The QQ plots show that the lognormal model fits better than the linear
> model, but still much worse than the GAMLSS. So, in my opinion, the AIC
> of the lognormal model should be between the AICs of the both other
> models. What happens here?
> Btw: For the lognormal model, I transformed the response variable by
> log(). Apart from that, I used the same formula as for the linear model.
So you got the AIC for the logged data, which is not comparable to the
others. You need to convert to a likelihood and hence AIC for the
original data. (I think anyone using AIC needs to know how to do that, as
it is part of the basic understanding of what a likelihood is. It is also
part of the derivation of the estimation of the Box-Cox transformation,
something which you might well want to consider here.)
--
Brian D. Ripley, ripley at stats.ox.ac.uk
Professor of Applied Statistics, http://www.stats.ox.ac.uk/~ripley/
University of Oxford, Tel: +44 1865 272861 (self)
1 South Parks Road, +44 1865 272866 (PA)
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