 GLMMs are generally defined as such that conditioned on the random effects, formula_1, the dependent variable, formula_2, is distributed according to an exponential family.Where formula_7 and formula_8 are the fixed effects design matrix, and fixed effects; formula_9 and formula_1 are the random effects design matrix and random effects.The complete likelihood,
has no general closed form, and integrating over the random effects is usually extremely computationally intensive.