A Standardization Procedure to Incorporate Variance Partitioning Based Priors in Latent Gaussian Models

TL;DR

This paper introduces a standardization procedure that extends variance partitioning priors to a wider range of Latent Gaussian Models, improving prior elicitation and model interpretability.

Contribution

The work presents a novel standardization method enabling variance partitioning priors to be applied to both fixed and random effects in LGMs, including IGMRFs.

Findings

Standardization improves prior elicitation in LGMs.

Method demonstrated with simulated and real survival data.

Enhanced applicability of VP priors to diverse models.

Abstract

Latent Gaussian Models (LGMs) are a subset of Bayesian Hierarchical models where Gaussian priors, conditional on variance parameters, are assigned to all effects in the model. LGMs are employed in many fields for their flexibility and computational efficiency. However, practitioners find prior elicitation on the variance parameters challenging because of a lack of intuitive interpretation for them. Recently, several papers have tackled this issue by rethinking the model in terms of variance partitioning (VP) and assigning priors to parameters reflecting the relative contribution of each effect to the total variance. So far, the class of priors based on VP has been mainly deployed for random effects and fixed effects separately. This work presents a novel standardization procedure that expands the applicability of VP priors to a broader class of LGMs, including both fixed and random effects. We describe the steps required for standardization through various examples, with a particular focus on the popular class of intrinsic Gaussian Markov random fields (IGMRFs). The practical advantages of standardization are demonstrated with simulated data and a real dataset on survival analysis.