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I'm working on a project where I'd like to compare the performance of BYM latent models as run in three different software packages (winBUGS, CARBayes, and R-INLA) on the same data. Part of this involves trying to create as much comparability between the three models as possible -- such as trying to specify the same prior distributions for parameters in the BYM models.

So far, I've been able to do a decent job of this between winBUGS and CARBayes. However in R-INLA (which I'm new to), I'm running into a problem; I'd like to specify a gamma distribution for a prior, but the R-INLA only has a log-gamma distribution option. I see from here that's it's possible to create one's own prior distributions for use in R-INLA models, but I'm a bit unclear about how to actually do this.

Here's an example of what I have for my R-INLA code at the moment for my BYM model (I'm modeling count data with a Poisson likelihood):

###My model### 
form_INLA<-O~1+offset(log(E))+depriv+ f(London_data$idx, model = "bym", graph = adj, 
      hyper = list(prec.unstruct = list(prior = "loggamma", param = c(0.001, 0.001)), ###prior specification###
                    prec.spatial = list(prior = "loggamma", param = c(0.1, 0.1)))) ###prior specification###

###Run the model###
    INLA_BYM <- inla(form_INLA, family = "poisson", data = as.data.frame(London_data), 
                     control.compute = list(dic = TRUE), 
                     control.inla = list(tolerance = 1e-20, h = 1e-08), 
                     control.predictor = list(compute = TRUE)) 

Also, would any of you know if it's possible to set prior distributions in the R-INLA BYM model for parameters other than the random effects terms (i.e. for the intercept term and beta coefficient term)?

1 Answer 1

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INLA considers for the precision parameter tau the following distribution log(tau) ~ logGamma(a,b). In this way tau follows a gamma distribution as in Winbugs, but the log trasformation ensures a correct value for the parameter.

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