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+# Alligators: multinomial - logistic regression
+# http://www.openbugs.info/Examples/Aligators.html
+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
+
+ # Fit standard Poisson regressions relative to baseline
+ lambda[i, j] ~ dflat() # 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]
+ culmative.X[i, j, k] <- culmative(X[i, j, k], X[i, 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
+ }
+ }
+}