If you're willing to settle for Wald tests this should work:
gm1 <- glmer(cbind(incidence, size - incidence) ~ period + (1 | herd),
data = cbpp, family = binomial)
However, note (from
The designations "type-II" and "type-III" are borrowed from SAS,
but the definitions used here do not correspond precisely to those
employed by SAS. Type-II tests are calculated according to the
principle of marginality, testing each term after all others,
except ignoring the term's higher-order relatives; so-called
type-III tests violate marginality, testing each term in the model
after all of the others. This definition of Type-II tests
corresponds to the tests produced by SAS for analysis-of-variance
models, where all of the predictors are factors, but not more
generally (i.e., when there are quantitative predictors). Be very
careful in formulating the model for type-III tests, or the
hypotheses tested will not make sense.
I would check your results very carefully to make sure they make sense!
Alternatively, you can use
afex::mixed to get analogous tables via likelihood ratio test or parametric bootstrap; the latter is the most accurate, but also the slowest by far.
?pvalues in the
lme4 package for more general discussion of p-value computation in the context of GLMMs.