A standardization procedure to incorporate variance partitioning‐based priors in latent Gaussian 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 representing 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 applied to 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. The practical advantages of standardization are demonstrated with simulated data and a real dataset on survival analysis.