Robustness, model checking and latent Gaussian models

TL;DR

This paper develops a framework for model checking and robustness analysis specifically tailored for latent Gaussian models, addressing the challenge of verifying assumptions about latent parameters.

Contribution

It introduces discrepancy measures based on alternative models and promotes a workflow for model criticism and robustness assessment in LGMs.

Findings

Effective methods for checking latent Gaussianity assumptions.

Tools implemented in Stan and R-INLA for practical application.

Enhanced understanding of model assumption impacts.

Abstract

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.