  The ability to generate samples of the random effects from their conditional
distributions is fundamental for inference in mixed effects models. Random walk
Metropolis is widely used to perform such sampling, but this method is known to
converge slowly for medium dimensional problems, or when the joint structure of
the distributions to sample is spatially heterogeneous. The main contribution
consists of an independent Metropolis-Hastings (MH) algorithm based on a
multidimensional Gaussian proposal that takes into account the joint
conditional distribution of the random effects and does not require any tuning.
Indeed, this distribution is automatically obtained thanks to a Laplace
approximation of the incomplete data model. Such approximation is shown to be
equivalent to linearizing the structural model in the case of continuous data.
Numerical experiments based on simulated and real data illustrate the
performance of the proposed methods. For fitting nonlinear mixed effects
models, the suggested MH algorithm is efficiently combined with a stochastic
approximation version of the EM algorithm for maximum likelihood estimation of
the global parameters.
