Fitting double hierarchical models with the integrated nested Laplace approximation

Abstract Double hierarchical generalized linear models (DHGLM) are a family of that flexible enough as to model hierarchically the mean and scale parameters. In Bayesian framework, fitting highly parameterized is challenging when this problem addressed using typical Markov chain Monte Carlo (MCMC) methods due potential high correlation between different parameters effects in model. The integrated nested Laplace approximation (INLA) could be considered instead avoid dealing with these problems. However, DHGLM do not fit within latent Gaussian random field (GMRF) INLA can fit. paper, we show how by combining importance sampling (IS) algorithms. particular, will illustrate split into submodels fitted so remainder adaptive multiple IS (AMIS) aid graphical representation This illustrated simulation study on three types two real data examples.