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?

- Operating System: Windows 10
- brms Version: 2.20.4

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.

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