[R] quasipoisson, glm.nb and AIC values

[ripley@stats.ox.ac.uk]

On Wed, 12 Mar 2003, kjetil brinchmann halvorsen wrote:

> On 12 Mar 2003 at 19:50, Uwe Ligges wrote:

> > I would vote against comparing different model classes using AIC.
> 
> Why? I thought one of the advantages with AIC is that it can be used 
> to compare different model classes, although in practice it might be 
> difficult because programs delete constants which shouldn't be 
> deleted.

On the last point, as log-likelihood is only defined up to a constant
(depending on the dominating measure and hence the data), it is more a
question of legitimate use of different definitions by different
programmers.  In this case it is a question of using method inherited from
glm that an inappropriate in R (but not in S) and I will fix it for R 
1.7.0.

On the first point: Akaike only defined AIC for a nested series of models.
AIC can be used to compare non-nested models, but

1) The theory needs to make assumptions which may well not hold, for 
example when comparing lme models with lm or gee models when under one 
model the MLEs fitting the other are on the boundary of the space.

2) The sampling variability of the difference in AIC is large in the
non-nested case.

See e.g.
http://www.stats.gla.ac.uk/~goeran/euroworkshop/webpages/2002/slides/brian.pdf

-- 
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