Identifying link functions for gamma glmm

   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?

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