[R-sig-ME] compare fit of GLMM with different link/family

[Ben Bolker]

On 1/26/22 12:15 PM, Don Cohen wrote:
> 
> not sure this should be sent to r-sig-mixed-models using r-project.org,
> feel free to post it there if so
> 
>   >    I would say that in general it's OK to compare models with different
>   > links, families, etc. via AIC *as long as you don't explicitly transform
>   > the response variable* -- i.e. you have to be careful comparing
>   >
>   >   lm(log(y) ~ ....)
>   >
>   > with
>   >
>   >    lm(y ~ ...)
>   >
>   > (you need a Jacobian term in the AIC expression to account for the
>   > change in scaling of the density), but comparing basically
> 
> This doesn't make any sense to me.
> There are only two parts to AIC, log liklihood and a parameter
> correction.  What does this transform have to do with either?
> If you get a better loglik for the transformed version I'd just
> say that model fits the data better.
> (Whereas the parameter correction has to do with what you think
> makes a model better outside of fit to data, and is more subjective.)
> 
> Actually I do have a complaint about loglik -- I think it would
> be fixed by really computing the probability of response given
> inputs, and that this could be done pretty easily by simply
> admitting that the responses are not exact measurements, and
> changing them to ranges or at worst distributions.  Could THAT
> be related to the transform problem?  If so then this seems like
> a solution.
> 
> Perhaps you can give me a reference to what I'm missing.
> I also don't see what nested models have to do with this.

-- 
Dr. Benjamin Bolker
Professor, Mathematics & Statistics and Biology, McMaster University
Director, School of Computational Science and Engineering
(Acting) Graduate chair, Mathematics & Statistics