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.

双层次广义线性模型 (DHGLM) 是一系列模型，它们足够灵活，可以对均值和尺度参数进行分层建模。在贝叶斯框架中，当使用典型的马尔可夫链蒙特卡罗 (MCMC) 方法解决此问题时，拟合高度参数化的层次模型具有挑战性，因为模型中不同参数和效果之间可能存在高度相关性。可以考虑使用集成嵌套拉普拉斯近似 (INLA) 来避免处理这些问题。然而，DHGLM 不适合 INLA 可以适合的潜在高斯马尔可夫随机场 (GMRF) 模型。在本文中，我们展示了如何通过结合 INLA 和重要性采样 (IS) 算法来拟合 DHGLM 和 INLA。尤其是，我们将说明如何将 DHGLM 拆分为可以用 INLA 拟合的子模型，以便借助分层模型的图形表示使用自适应多重 IS (AMIS) 来拟合其余参数。使用对三种不同类型的模型和两个真实数据示例的模拟研究来说明这一点。