[R] Account for a factor variability in a logistic GLMM in lme4

[Pedro Vaz]

We did a field study in which we tried to understand which factors
significantly explain the probability of a group of animals (5 species in
total) crossing through 30 wildlife road-crossing structures. The response
variable is binomial (yes=crossed; no = did not cross) and was recorded by
animal species. We did about 30 visits to each crossing structure (our
random factor) in which we recorded the binomial response by each animal
species and the values of a few predictors.

So, I have this (simplified for better understanding) mixed effects model:
library (lme4)

Mymodel <- glmer(cross.01 ~ stream.01 + width.m + grass.per + (1|structure.id),
  data = Mydata, family = binomial)

stream is a factor with 2 levels; width.m is continuous; grass.per is a
percentage

This is the model in which I assessed crossings by all species combined
(i.e., cross. 01 = 1 when an animal of any species crossed, cross.01 = 0
when no animal crossed). However, we did one model per species and those
species-specific models highlight that different species exhibit different
relationships between crossings and explanatory variables.

My problem: This means that my model above suffers from an additional
source of variation related to the species level without accounting for it.
However I cannot recalibrate the above model adding the species level as
random factor because, in my binomial response, the zero means no species
crossed (all zeros would have "NA" or, say, "none" for species) and so that
additional source of variation is only present when the response was 1.
Just to confirm this, I did add species as a random factor:

(1 | structure.id) + (1 | species)

As expected, the message is "Error: Response is constant"

How can I account for the species variability in my model in lme4?

A few more details:
A few more details:
- I had 5 mammal species crossing through the 30 road-crossing structures.
In 134 occasions (i.e., 134 of my records on individual
crossing-structures), no animal crossed (so, @Dimitris Rizopoulos, no, I
didn't have the species of the animals which did not cross. A "no cross"
was a "zero" for that visit to the crossing-structure). In 498 occasions,
at least one animal of a given species crossed the structure (these were my
"ones" in my logistic response)
- A side comment: This is to respond to a reviewer in a paper of mine,
i.e., I did and presented species-specific and "all combined species"
models in the draft reviewed but now the reviewer is asking me to control
for the species variability in the "combined species model". He asked me to
include a random factor but I realized that is not possible since all my
zeros would have "none" for the species that crossed. So, is it possible to
control for the species variability in my model in lme4 in another way? I
know in nlme including a fitting of variance structures it's not that
difficult...
- Every time an animal crossed, the binary response was "one" and I
recorded the animal species as well. Thus, I have variability between
species in the "ones" but not in my "zeros" of my logistic model.

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