# Code for the one-way ANOVA of the ant nest data (Gotelli & Ellison 2004, Chapter 5). model {for (i in 1:N) {x[i] ~ dnorm(lambda[T[i]],tau)} # # Enter prior estimate of among-group variance s0 into the formula for precision (tau) # as dgamma(nu/2, nu*s0/2), where # nu is the "strength of belief", expressed as an integer "degrees of freedom" # variance =1/precision. # An uninformative prior on precision would be dgamma(0.0001, 0.0001) # hence in an uninformative prior, precision is small and variance is very large. # # Example: estimate prior variance as 1 with modest belief (nu = 2) # enter tau ~ dgamma(1, 1) tau ~ dgamma(5,5) s2 <- 1/tau #Alternatively, priors could be uninformative tau ~ dgamma(0.001,0.001) s2 <- 1/tau # BE SURE TO COMMENT OUT THE PRIORS YOU DON'T WANT! # Enter prior estimates for within-group means for lambda[1] and lambda[2] # Here, lambda[i] is assumed normal; for "sharp" initial estimates of lambda, set # lambda[i] ~ dnorm(prior estimated mean, prior estimated variance), where # prior estimated mean is initial estimate, and prior estimated variance is small. # Increasing the value for prior estimated within-group variance reflects a lower # confidence in the prior estimate lambda[1] ~ dnorm(5,0.001) lambda[2] ~ dnorm(15,0.001) #Alternatively, priors on lambda could be uninformative by substituting the following line #for the first line of the 'for loop' in the next section. for (i in 1:G) {lambda[i] ~ dnorm(0,0.001) # BE SURE TO COMMENT OUT THE PRIORS YOU DON'T WANT! for (i in 1:G) {wlam[i] <- lambda[i]*K[i] delta[i] <- lambda[i]-lambda.G s.delta[i] <- K[i]*pow(delta[i],2)} lambda.G <- sum(wlam[])/sum(K[]) s1 <- sum(s.delta[1:G]) Fhat <- s1/(s2*G-s2) # compare Fhat to 5% sig level for F(1,8) test <- step(Fhat-5.32)} Data list(x=c(9,6,4,6,7,10,12,9,12,10), T=c(1,1,1,1,1,1,2,2,2,2), K=c(6,4), G=2,N=10) #For one chain... Inits list(tau=1)