Orthogonal matrices-time component

[Molly Cliff]

Hi all,

I was recently discussing an issue with a colleague regarding my INLA modeling, where I'm using a space-time model to predict binary outbreak presence. When I add covariates to the model, I don’t see a significant improvement in WAIC, DIC, or predictive performance.

My colleague suggested that this might be due to collinearity between the covariates and the spatial component of the model, and mentioned the use of orthogonal matrices  as a potential solution. I'm wondering whether similar collinearity could also be occurring with the temporal component of the model, and if so, whether the same orthogonal strategy would apply.

The spatial and temporal component of the model can be seen below:

form5 <- outbreak_occur ~ f(month, model = "ar1", cyclic = TRUE) +
  f(ID.year1, model = "iid") +
  f(ID.area, model = "bym2", graph = ken.adj,  hyper = "shyper",scale.model = TRUE, constr = TRUE)

M5 <- inla(
  form5,
  data = bf1,  
  family = "binomial",  
  control.predictor = list(compute = TRUE),
  control.compute = list(dic = TRUE, waic = TRUE, cpo = TRUE, config = TRUE)
)

 The response variable is binary (presence/absence of outbreak), and the outcome is very sparse. I'm trying to add additional covariates  (e.g., humidity, wind, AOD) as fixed effects.

Could anyone point me toward relevant resources,/best practices on how to address collinearity between covariates and the structured space or time components in INLA?

All the best,

Molly