[R] comparing AIC values of models with transformed, untransformed, and weighted variables
Prof Brian Ripley
ripley at stats.ox.ac.uk
Mon Mar 27 17:43:46 CEST 2006
Two comments:
1) The log-likelihood and hence AIC for a model for log X are not
comparable with those of a model for X. You need to make an additive
adjustment when you transform: it is quite easy to work out what from the
definitions.
2) The AIC given by glm() for weighted models was wrong in R < 2.3.0
alpha. I am not sure why you are using a glm for what appears to be a
least-squares fit: use lm() instead (or try 2.3.0 alpha).
On Wed, 15 Mar 2006, Patrick Baker wrote:
> Hi there, I have a question regarding model comparisons that seems simple
> enough but to which I cannot find an answer. I am interested in developing a
> predictive model relating some measure of a tree's stem to the total leaf
> area (TLA) of the tree. Predictor variables might include, for example, the
> total cross-sectional area of the tree (commonly referred to as basal area)
> or the amount of sapwood area (SA) (which represents the amount of wood
> involved in active transport of water up the tree to the leaves). A variety
> of people have developed these models for a variety of tree species in a
> variety of places around the world. Perhaps not surprisingly, different
> studies have used different model forms in analyzing their data. I am
> interested in comparing the range of models that have been previously used
> (some of which are theoretically derived, others of which are empirically
> driven) using a data set that I have collected (for yet another species in
> yet another place). To compare the different model forms I had intended to
> use the AIC. However, I have found, again perhaps not surprisingly, that when
> I use log-transformed data, the AIC is substantially lower for a given
> predictor variable. If I use a weighted glm the same issue arises. For
> example, using BA vs TLA the (rounded) AIC values are 275 for a linear
> model, 30 for a log-log model, and 8 for a glm weighted by 1/BA. I don't
> believe that these vast differences reflect a major improvement in the model,
> but rather the scaling of the variables by transformation or weighting. What
> I'd like to get some advice or insight on is whether there is an appropriate
> way to rescale the AIC values to permit comparisons across these models. Any
> suggestions would be very welcome. Cheers, Patrick Baker
>
--
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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