binomial fixed-effect p-values by simulation

We read, e.g. in Pinheiro and Bates, that one situation where
fixed-effect LRTs are anti-conservative is when the number of fixed
effect parameters being tested is large with respect to the number of
groups.

In the tests I'm doing, there's only a single binary fixed effect
factor being tested - a between-subjects factor like gender, as noted
earlier.

I'm finding evidence for pretty serious anti-conservatism here too
(e.g. LRT chi-square p=0.0001 vs. LRT simulation p=0.016), and I'm
working on some reproducible code to demonstrate this.