model
{
# PRIORS
alpha[1] <- 0; # zero contrast for baseline food
for (k in 2 : K) {
alpha[k] ~ dnorm(0, 0.00001) # vague priors
}
# Loop around lakes:
for (k in 1 : K){
beta[1, k] <- 0
} # corner-point contrast with first lake
for (i in 2 : I) {
beta[i, 1] <- 0 ; # zero contrast for baseline food
for (k in 2 : K){
beta[i, k] ~ dnorm(0, 0.00001) # vague priors
}
}
# Loop around sizes:
for (k in 1 : K){
gamma[1, k] <- 0 # corner-point contrast with first size
}
for (j in 2 : J) {
gamma[j, 1] <- 0 ; # zero contrast for baseline food
for ( k in 2 : K){
gamma[j, k] ~ dnorm(0, 0.00001) # vague priors
}
}
# LIKELIHOOD
for (i in 1 : I) { # loop around lakes
for (j in 1 : J) { # loop around sizes
# Multinomial response
# X[i,j,1 : K] ~ dmulti( p[i, j, 1 : K] , n[i, j] )
# n[i, j] <- sum(X[i, j, ])
# for (k in 1 : K) { # loop around foods
# p[i, j, k] <- phi[i, j, k] / sum(phi[i, j, ])
# log(phi[i ,j, k]) <- alpha[k] + beta[i, k] + gamma[j, k]
# }
# Fit standard Poisson regressions relative to baseline
lambda[i, j] ~ dnorm(0, 0.00001) # vague priors
for (k in 1 : K) { # loop around foods
X[i, j, k] ~ dpois(mu[i, j, k])
log(mu[i, j, k]) <- lambda[i, j] + alpha[k] + beta[i, k] + gamma[j, k]
}
}
}
# TRANSFORM OUTPUT TO ENABLE COMPARISON
# WITH AGRESTI'S RESULTS
for (k in 1 : K) { # loop around foods
for (i in 1 : I) { # loop around lakes
b[i, k] <- beta[i, k] - mean(beta[, k]); # sum to zero constraint
}
for (j in 1 : J) { # loop around sizes
g[j, k] <- gamma[j, k] - mean(gamma[, k]); # sum to zero constraint
}
}
}