Hello,
     Thanks to everyone who contributes to this list!  I often find random
questions I have answered in the archives of this list.

My specific question of the moment, a simplified example of what I'm doing
that I hope illustrates my question...

     If we have a poisson-distributed response variable in a mixed model
such as called by:

lmer(amrotot ~ year + (year|route), family=poisson(link=log))

    where amrotot is an integer count, year is, well, the year (as a linear
predictor, not a factor) and route is a sampling unit.  If 'exposure' varies
by route, we can define another model with an offset such as:

lmer(amrotot ~ year + (year|route), offset=effort, family=poisson(link=log))

     this all seems, generally good and fine.  A colleague asked me why not
use (amrotot/effort) as the response variable, but this of course results in
a non-integer response variable.  Yet it turns out, lmer (or glm, for that
matter) will indeed estimate a model using the non-integer response variable
(amrotot/effort) but gives warnings.  I understand that poisson regression
assumes a poisson-distributed integer response variable, but I was curious
about *why* lmer would provide results for non-integer response variables
such as (amrotot/effort) and if these results are valid or somehow
comparable to results where amrotot is the response and effort is an offset,
with special reference to the confidence intervals of the random effects.
Using non-integer response variables in poisson regression looks and seems
wrong to me, but IANA statistician and maybe lmer is doing something I don't
quite get to make this work.

Thank you!

Best,
Dan Barton

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