Short summary of the problem
I am a total beginner in spatial modeling and brms. My data is the proportion of land cover per unit area data with a certain amount of zero and one values. So, I am trying to fit a zero-one inflated beta model in brms. I am also trying to account for the spatial autocorrelation using ICAR. But I am confused about which terms the CAR should be added to, i.e., mu, phi, zoi, coi?
Adding to mu will model spatial autocorrelation in the expectation of the continuous responses, but not in the probabilities of zero or one. Adding to zoi will model spatial autocorrelation in whether an observation comes from the continuous process or one of the inflation states. Adding to coi will model spatial autocorrelation in whether an observation is a zero or a one, conditional on that observation being in one of the inflation states. Adding to phi will model correlated spatial variation in the scale parameter of the continuous part of the response.
If you wanted to model, for example, spatial autocorrelation in the probability of being a zero, as distinct from both the continuous and the one-inflated components, and NOT spatial autocorrelation in the probability of being a one as distinct from the continuous component, you would need to reparamterize the zero-one inflated beta using a custom family. If you’re sure that’s what you need, we can help you with that, but let’s not cross that bridge unless you’re sure.