  We introduce a new copula-based correction for generalized linear mixed
models (GLMMs) within the integrated nested Laplace approximation (INLA)
approach for approximate Bayesian inference for latent Gaussian models. While
INLA is usually very accurate, some (rather extreme) cases of GLMMs with e.g.
binomial or Poisson data have been seen to be problematic. Inaccuracies can
occur when there is a very low degree of smoothing or "borrowing strength"
within the model, and we have therefore developed a correction aiming to push
the boundaries of the applicability of INLA. Our new correction has been
implemented as part of the R-INLA package, and adds only negligible
computational cost. Empirical evaluations on both real and simulated data
indicate that the method works well.
