Model checking is essential to evaluate the adequacy of statistical models and the validity of inferences drawn from them. Particularly, hierarchical models such as latent Gaussian models (LGMs) pose unique challenges as it is difficult to check assumptions about the distribution of the latent parameters. Discrepancy measures are often used to quantify the degree to which a model fit deviates from the observed data. We construct discrepancy measures by (a) defining an alternative model with relaxed assumptions and (b) deriving the discrepancy measure most sensitive to discrepancies induced by this alternative model. We also promote a workflow for model criticism that combines model checking with subsequent robustness analysis. As a result, we obtain a general recipe to check assumptions in LGMs and the impact of these assumptions on the results. We demonstrate the ideas by assessing the latent Gaussianity assumption, a crucial but often overlooked assumption in LGMs. We illustrate the methods via examples utilising Stan and provide functions for easy usage of the methods for general models fitted through R-INLA.

翻译：模型检验对于评估统计模型的充分性以及从中得出的推论的合理性至关重要。特别是，隐高斯模型（LGM）等分层模型因其难以检验隐参数分布的假设而面临独特挑战。通常使用差异度量来量化模型拟合与观测数据的偏离程度。我们通过以下方式构建差异度量：（a）定义具有放宽假设的替代模型；（b）推导对该替代模型所引发的差异最为敏感的差异度量。同时，我们提倡一种结合模型检验与后续鲁棒性分析的模型批评工作流程。由此，我们获得了一个通用方法，用于检验LGM中的假设以及这些假设对结果的影响。我们通过评估隐高斯性假设（LGM中一个关键但常被忽视的假设）来展示这一思路。我们利用Stan实现示例以阐述这些方法，并提供函数以便通过R-INLA对通用模型进行简便应用。