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I have computed two models using INLA and following the proceedure laid out in this paper.

As in the paper, the model has two random effects, one representing temporal relationships between data points, and one representing spatial relationships. Both are inserted into the model as precision matrices within the random effects. There are no fixed effects in the model.

I wanted to see how much variance each relationship would explain independently, to determine how much covariation there was between time and spatial relationships. To do this, I thought I could run a model with only the temporal random effect, and only the spatial random effect, then compare them with the model containing both processes to see how much worse their predictions are to the full model. I compared the models using WAIC.

However, the WAIC values I have got are incredibly variable: e.g.

temporal model: -4912.38

spatial model: 2453.91

temporal and spatial model: -5967.42

Why might this be? My best guess is that is something to do with how the structured random effects are implemented, but I am not entirely sure why. Could anyone offer some reading or advice?

I don't think there is anything wrong with how the models are calculated / estimated (all other indicators suggest the model is fine).

SamPassmore
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    It''s odd that you have positive AIC for one of the models and negative for the others. Anyway, since you seem to be interested in prediction, why don't you use a measure of predictive accuracy such as mean squared error ? – Robert Long Dec 03 '20 at 20:21
  • WAIC might not be the best estimator for random effects models. See Section 4.2 here: https://avehtari.github.io/modelselection/roaches.html. In that case, a k-fold CV might be a better alternative, if you can afford the computational burden. – gregorp Aug 09 '21 at 08:30

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