model definition issues for repeat measures

Caroline <charris at ...> writes:

I am trying to analyse my count data using lmer, family=poisson, however
this model is unable to cope with my data as the count data for one of my
factor levels drops to zero for every data point. The model runs without any
error messages, however one interaction term has a huge Std error and is not
significant (corresponding to the data points which are all zero), when it
clearly should be significant from looking at the data graphically.

Please can you advise the best way forward to analyse the data. Please find
my data table and R script attached. 

Thank you for including a reproducible example! Although in this case I
think it's probably not necessary.  You should look up/Google for
"Hauck-Donner effect" (you can find a discussion in Venables and Ripley's
book), which refers to the situation where the approximation used to
compute confidence intervals on GLM(M)s breaks down for strong effects.
You should use explicit model comparison (?update, ?anova, ?drop1) to
test the difference between models with and without the intercept term.

However, you might want to be careful with the all-zero case, as it will
lead to an infinite estimate (in theory) of the interaction coefficient --
in practice it will just lead to a very large, poorly constrained estimate.
You could try a Bayesian method, or you could just try leaving out that
category and make sure that the qualitative results of your analysis
remain unchanged ...

  Ben Bolker