[R] AIC for lognormal model

Prof Brian Ripley ripley at stats.ox.ac.uk
Sat Aug 5 20:08:36 CEST 2006

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)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595

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