in glm output Akaike Information Criterion is computed dividing the usual
formula by N (number of observations).
When a covariate is included in a model (for example a Poisson model), the
number of observations can obviously change. So there's two possibilities:
Compare two modes with the usual AIC, limiting observations to the smaller
sample of observations (that one with new covariate included),
Compare two models with AIC as in the glm output, ignoring the different
number of observations between two models. In this case models are not
nested, but AIC is specifically addressed to compare non nested models.
Using two strategies above, conclusions can change and different models can
be selected.
So the question is :
In comparing two models should we use second AIC (as in glm output) and
second strategy or there's some case where first strategy has to be
preferred and vice versa?
