Treffer: Robustness, model checking, and hierarchical models.

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 on the latent parameters. Diagnostic statistics are often used to quantify the degree to which a model fit deviates from the observed data. We construct diagnostic statistics by (a) defining an alternative model with relaxed assumptions and (b) deriving the diagnostic statistic 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 hierarchical models 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 utilizing Stan and provide functions for easy usage of the methods for general models fitted through R-INLA. [ABSTRACT FROM AUTHOR]

Copyright of Journal of the Royal Statistical Society: Series B (Statistical Methodology) is the property of Oxford University Press / USA and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)