Generalized Linear Mixed (effects) Models are typically used for modeling non-independent non-normal data (eg, longitudinal binary data).
GLMMs are a broad class of models: both linear mixed effects models and generalized linear models can be understood as special cases of GLMMs. GLMMs handle non-independence by including random effects. GLMMs are often contrasted with Generalized Estimating Equations, which may offer alternative approaches in many cases.
gllamm. Multilevel-analysis is an encompassing class of models. Mixed-effect and random-effects-model are used to describe a regression-like model in which the fixed effects of covariates are augmented with random effects, to be intergrated out in ML or REML estimation. Mixed-model is a linear model with a Gaussian response.
R implementation in
lme4 package of mixed models and GLMMs, respectively.
stata implementation of GLMMs.