Intuitive principle-based priors for attributing variance in additive model structures
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Variance parameters in additive models are often assigned independent priors that are selected haphazardly from simple parametric families. We present a new framework for constructing joint priors for the variance parameters that treats the model structure as a whole. The focus is latent Gaussian models where penalised complexity priors can be computed exactly and generalised to a principled-based joint prior. The prior distributes the total variance of the model components to the individual model components following a tree structure using intuitive hyperparameters. The hyperparameters can be set based on expert knowledge or be weakly informative, and the prior framework is applicable for software for Bayesian inference such as the R packages INLA and RStan. Three simulation studies show that with hyperparameters set to give weakly informative priors, the new prior performs comparably to or better than current state-of-the-art default prior choices according to carefully chosen application-specific measures. We demonstrate practical use of the new framework by analysing spatial heterogeneity in neonatal mortality in Kenya in 2010-2014 based on complex survey data. Overall, the new framework provides computationally efficient, proper, robust and interpretable priors where a priori assumptions for how variance is attributed to the model components is more transparent than independent priors.
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