Modeling precision (phi) with covariates in a spatial Beta regression using R-INLA

[João Marcos]

I am trying to fit a spatial Beta regression model where I need to model both the mean mu and the precision parameter phi simultaneously.

Specifically, my model formulation is:

Yi ~ Beta(mu_i,phi_i)

For the mean mu_i, I have a standard linear predictor with a spatial effect delta_i:

logit(mu_i) = kap_0 + kap_1*X1 + delta_i

For the precision phi_i, I do not have a spatial effect, but I need to include a continuous covariate V_i

log(phi_i) = lam_0 + lam_1*V1

I know that R-INLA easily handles the spatial linear predictor for the mean, but typically treats the precision parameter of the Beta family as a global hyperparameter. Is there any native or experimental way in R-INLA to model the precision parameter of a Beta distribution as a function of continuous covariates? 

[Helpdesk (Haavard Rue)]

it can be done but is not implemented. the easy way out is to write your own
beta-likelihood in C, see

inla.doc("cloglike")

the 'mu_i' will come from the linear predictor given in the formula, while you
need to add that 'log(phi_i)' depends on a covariate

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Håvard Rue
he...@r-inla.org