Fitting Double Hierarchical Models with the Integrated Nested Laplace Approximation

TL;DR

This paper introduces a novel approach combining INLA and importance sampling to efficiently fit double hierarchical generalized linear models, overcoming challenges faced by traditional MCMC methods.

Contribution

It presents a new method to fit DHGLM using INLA combined with importance sampling, enabling efficient Bayesian inference for complex hierarchical models.

Findings

Successful application to simulated data and real datasets

Improved computational efficiency over traditional MCMC methods

Effective splitting of models into submodels for INLA fitting

Abstract

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