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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
- }
- }
-}