[R-sig-ME] Identifying link functions for gamma glmm

Tahsin Ferdous t@h@|n|erdou@uo|c @end|ng |rom gm@||@com
Sat Nov 20 02:18:56 CET 2021

Dear Dr Ben,

Thanks a lot for the valuable information. At first, I tried to fit a glm
with a log link. I attached the residual vs fitted plot of this model. I
have seen an outlier in the plot (I am not sure what is meant by 300 in
this plot?). Should we always look at the diagnostic plots (residual vs
fitted) for glm, glmm or gee? If I run the model with the outlier, does it
give valid results?

Kindest regards,


On Fri, Nov 19, 2021 at 5:40 PM Ben Bolker <bbolker using gmail.com> wrote:

>    Most of the time I would suggest choosing link functions on
> scientific grounds, i.e. what scale makes sense for the expected
> effects? Link functions change the expected relationship with continuous
> predictors (do I expect the effects of predictors to be linear
> (identity), exponential (log), or hyperbolic (inverse)?) and change the
> meaning of interactions (does the value of one variable change the
> expected effect of the other additively (identity), proportionally
> (log), or ?? (inverse)).
>    I generally find that log links are more numerically stable (both
> identity and inverse links can sometimes lead to negative predictions).
> Logs are also nice because they essentially split the difference between
> the identity and inverse links.  If I have (say) responses that are time
> intervals, then analyzing on the identity scale describes additive
> effects on the time scale; analyzing on the inverse scale describes
> additive effects on the rate or speed (1/time) of the response;
> analyzing on the log scale describes proportional changes in *either*
> time or rate (because log(time) = -1*log(1/time)).
>    My general procedure would be to use a log link and see if the
> diagnostics detected any problems.
>    That said, you could use AIC or cross-validation if you are primarily
> interested in prediction (and aren't worried about snooping).
> Cross-validation will be slower but more reliable, *if* you are careful
> to maintain independence structure when you specify your training and
> testing sets (i.e., you should sample by levels of your grouping
> variable, not by individual observations)
> On 11/19/21 3:38 PM, Tahsin Ferdous wrote:
> > I am running a generalized linear mixed model with a gamma family. How
> can
> > I understand which link function I should use (log link, identity link,
> or
> > inverse link)? I tried to plot observed vs fitted values plots. But they
> > look similar? Should I look at AIC? If I fit a gamma glm, should I also
> > look at AIC to know which link function I should use in my model?
> >
> > If I fit gamma GEE . should I look at QIC for choosing the appropriate
> > model with link function?
> >
> >       [[alternative HTML version deleted]]
> >
> > _______________________________________________
> > R-sig-mixed-models using r-project.org mailing list
> > https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
> >
> --
> Dr. Benjamin Bolker
> Professor, Mathematics & Statistics and Biology, McMaster University
> Director, School of Computational Science and Engineering
> (Acting) Graduate chair, Mathematics & Statistics
> _______________________________________________
> R-sig-mixed-models using r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models

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