Adaptive spatiotemporal model

[MUHAMMED TAHIR MUHAMMED]

Hello Professors,

I am trying to run an adaptive spatiotemporal using year 2010, 2015, 2018 and 2021. However, the spatial weight for each year are different (adaptive).

In my methodology, I combined the four different precision matrices, Q_i  of same dimensions into block matrices in the diagonal of a single precision matrix Q_full with AR(1) at off diagonal.

My model specification is:

# INLA model
formula <- response ~ 1 + covariate1 + covariate2 +
  f(region, model = "bym2", graph = adjacency_graph) +  
  f(time, model = "ar1") +  
  f(interaction_idx, model = "generic0", Cmatrix = Q_full) .

My inquiries are: Is this model specification and combination of the four precision matrices into one full precision inline with practice in the spatial statistics domain? Secondly, using the graph of a single year "adjacency_graph" instead of "Q_full" as used in the model above correct?

PLEASE I REALLY NEED EXPERT OPINION ON THIS WORK.

Regards,

Muhammed