Bayesian disease mapping, yet if undeniably useful to describe variation in risk over time and space, comes with the hurdle of prior elicitation on hard-to-interpret random effect precision parameters. We introduce a reparametrized version of the popular spatio-temporal interaction models, based on Kronecker product intrinsic Gaussian Markov random fields, that we name the variance partitioning model. The variance partitioning model includes a mixing parameter that balances the contribution of the main and interaction effects to the total (generalized) variance and enhances interpretability. The use of a penalized complexity prior on the mixing parameter aids in coding prior information in an intuitive way. We illustrate the advantages of the variance partitioning model using two case studies.
Keywords: Intrinsic Gaussian Markov random fields; Kronecker product Gaussian Markov random fields; intrinsic conditional autoregressive; penalized complexity prior; spatio-temporal smoothing.