Interpretation of random field in a Bernoulli/binomial model

[seananderson]

Questions by email:

If I fit a binomial model (dependent variable is either 0 or 1) [and there is a strong estimated spatial random field] does it mean that my dependent variable is spatially clustered, i.e. that the occurrence of 1s and 0s is spatially non-independent?

How do I find the log likelihood of the model?

[seananderson]

does it mean that my dependent variable is spatially clustered, i.e. that the occurrence of 1s and 0s is spatially non-independent?

Yes, after after accounting for the other effects in the model. One way to think about it is that there are spatially structured latent variables causing left-over spatial correlation in the occurrence of 1s and 0s after accounting for any other effects (usually fixed effects) you've explicitly included. The 1s and 0s are Bernoulli realizations of some underlying probability of 1s, which is modelled as a Gaussian Markov random field (likely in logit space).

Another part of the question was related to how to extract the log likelihood from the model. The simplest answer is to use the loglik() method on your model. The AIC() method uses that.