Spatial simultaneous autoregressive (SAR) structures in multilevel models


New user here!

In brms, we can impose spatial simultaneous autoregressive (SAR) structures on residuals using cor_errorsar with a spatial weighting matrix W, as follows:

brm(y ~ x, autocor = cor_errorsar(W))

Suppose that my data were grouped into, say, 10 groups, and my spatial weighting matrix was actually a 10x10 matrix specifying the spatial relationships between groups.

If I wanted to deal with grouping using random intercepts, could I continue to use cor_errorsar to deal with spatial relationships between groups? Perhaps by expanding my 10x10 matrix into a larger one, such that all individuals within the same group have identical spatial weights?

brm(y ~ x + (1 | group), autocor = cor_errorsar(W))

Or would I have to resort to another method, such as cov_ranef? Though I get the impression that this argument takes covariance matrices, not spatial weighting matrices.

Many thanks in advance!


You can continue to use cor_errorsar even if you add random intercepts for the grouping variable. It may just take longer to converge.


Thanks Paul!