  To account for measurement error (ME) in explanatory variables, Bayesian
approaches provide a flexible framework, as expert knowledge about unobserved
covariates can be incorporated in the prior distributions. However, given the
analytic intractability of the posterior distribution, model inference so far
has to be performed via time-consuming and complex Markov chain Monte Carlo
implementations. In this paper we extend the Integrated nested Laplace
approximations (INLA) approach to formulate Gaussian ME models in generalized
linear mixed models. We present three applications, and show how parameter
estimates are obtained for common ME models, such as the classical and Berkson
error model including heteroscedastic variances. To illustrate the practical
feasibility, R-code is provided.
