JAGS multiple linear regression with y[i] GAMMA (bayesian)

Question

I have a question about this model in JAGS, I want to make a bayesian linear regression with a y[i] that follows not a normal distribution but a gamma.

The model is this:

"model {
 Priors:
a ~ dnorm(0, 0.0001) # mean, precision = N(0, 10^4)
b ~ dnorm(0, 0.0001)
shape ~ dunif(0, 100)

 # Likelihood data model:
 for (i in 1:N) {
linear_predictor[i] <- a + b * x[i]
# dgamma(shape, rate) in JAGS:
y[i] ~ dgamma(shape, shape / exp(linear_predictor[i]))
 }
 }
 "

What should I change to make this code usable for a multiple linear regression with this data?

 dataListGamma = list(
   x = x,
   y = y,
   Nx = dim(x)[2],
   Ntotal = dim(x)[1]
 )

i'm receiving this error: Error in node (shape/(exp(linear_predictor[1331]))) how can this be possible? i cant understand if i run it again it changes the value that makes the problem

Answer 1

Something like this (making b a vector with identical, independent priors for each element, and constructing the linear predictor with a for loop) should work:

model {
# Priors:
a ~ dnorm(0, 0.0001) # mean, precision = N(0, 10^4)
for (j in 1:Nx)
    b[i] ~ dnorm(0, 0.0001)
}
shape ~ dunif(0, 100)

 # Likelihood data model:
 linear_predictor[i] <- a
 for (i in 1:Ntotal) {
    for (j in 1:Nx) {
       linear_predictor[i] <- linear_predictor[i] + b[j]*N[i][j]
    }
    y[i] ~ dgamma(shape, shape / exp(linear_predictor[i]))
  }
 }