[R-sig-ME] incorporating effort as an effect in binomial GLMM

[Ben Bolker]

  [this is not my question; it's posted on behalf of someone who wants
to remain anonymous ...]

I am testing the effect of a treatment to reduce bycatch in fishing
nets. Note the the design uses paired nets (control vs experiment)
soaked simultaneously but of different length (limited budget did no
allow to have an experimental net as long as control net).

The dependent variable are counts (no. individuals entangled), and I
have fishing effort and treatment (control vs experiment) as independent
variables. Since bycatch events were rare , the dataset is zero inflated
and positive catches are usually of 1 individual, therefore we switched
to a binomial model to test the probability of catching an individual
where if the catch is zero then probability =0, but if the catch is >0
then probability is a 1.
We used this model to predict bycatch probability in control and
experimental nets by setting fishing effort = 1.

There is an issue being raised, that Fishing effort being significantly
higher for control than experimental nets, the binomial model can yield
biased estimates of treatment and overestimate treatment efficiency.

I thought that including Effort as a fixed effect in the model would
mean that the model takes into account the difference in effort when
predicting the bycatch probability. Is that true?
However, I am not entirely sure HOW the glmer function does it and I
would like to know your opinion about the issue being raised."