  We give answer to an open problem regarding consistency of the maximum
likelihood estimators (MLEs) in generalized linear mixed models (GLMMs)
involving crossed random effects. The solution to the open problem introduces
an interesting, nonstandard approach to proving consistency of the MLEs in
cases of dependent observations. Using the new technique, we extend the results
to MLEs under a general GLMM. An example is used to further illustrate the
technique.
