论文标题
将双分层模型与集成的嵌套拉普拉斯近似拟合
Fitting Double Hierarchical Models with the Integrated Nested Laplace Approximation
论文作者
论文摘要
双分层通用线性模型（DHGLM）是一个足够灵活的模型家族，以层次对平均值和比例参数进行建模。在贝叶斯框架中，当使用典型的马尔可夫链蒙特卡洛（MCMC）方法解决此问题时，拟合高度参数化的层次模型是具有挑战性的，这是由于模型中不同参数和效果之间的潜在高相关性。可以考虑避免处理这些问题的集成嵌套拉普拉斯近似（INLA）。但是，DHGLM不适合INLA可以合适的潜在高斯马尔可夫随机场（GMRF）模型。 在本文中，我们将通过组合INLA和重要性采样（IS）算法来展示如何与INLA拟合DHGLM。特别是，我们将说明如何将DHGLM拆分为可以与Inla拟合的子模型，以便借助层次模型的图形表示，其余参数使用自适应倍数（AMI）拟合。使用对三种不同类型的模型和两个真实数据示例的仿真研究进行了说明。
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.
