Can you use a barrier model and model covariates for autocorrelation (kappa, tau)?

[Chris Smith]

Dear INLA community,

    Apologies for posting so many questions. This was a separate topic, and is also one I have been struggling to find an answer to in the literature.  I have read through the chapter on the barrier model in Advanced Spatial Modeling, and have a study area with several large lakes (ie. Lake Tahoe) that I would like to create a barrier across. I also have a strong need to model covariates on the spatial autocorrelation (kappa and tau), and am realizing that these are both non-stationary spatial random effects.   

form.barrier <- y ~ 0 + intercept + f(s, model = barrier.model)

formula <- y ~ 0 + f(i, model = spde)

My questions are:

1. Can you create one model using both of these spatial random effects? Does this create any problems for INLA? 

formula <- y ~ 0 + fixed effects + f(s,  model = barrier.model) + f(i, model = spde)

2. If they cannot be combined, I realize the older stationary method of just creating a 'hole' within the mesh with a polygon has theoretical problems (Neumann boundary conditions), but is it accurate enough to still use? I have 1-5 lakes that are <2% of my study area.

Thanks for any help you can give!

[Helpdesk (Haavard Rue)]

On Sat, 2025-11-22 at 10:25 -0800, Chris Smith wrote:
> My questions are:
> 1. Can you create one model using both of these spatial random effects? Does
> this create any problems for INLA? 
>
> formula <- y ~ 0 + fixed effects + f(s,  model = barrier.model) + f(i, model =
> spde)

sure, no problem.

--
Håvard Rue
he...@r-inla.org

[Chris Smith]

Thanks Dr. Rue!