Likelihood-based inference for generalized linear mixed models: Inference with the R package glmm

The R package glmm enables likelihood-based inference for generalized linear mixed models with a canonical link. No other publicly available software accurately conducts likelihood-based inference for generalized linear mixed models with crossed random effects. glmm is able to do so by approximating the likelihood function and two derivatives using importance sampling. The importance sampling distribution is an essential piece of Monte Carlo likelihood approximation, and developing a good one is the main challenge in implementing it. The package glmm uses the data to tailor the importance sampling distribution and is constructed to ensure finite Monte Carlo standard errors. In the context of the generalized linear mixed model, the salamander model with crossed random effects has become a benchmark example. We use this model to illustrate the complexities of the likelihood function and to demonstrate the use of the R package glmm.