Orange Trees: Non-linear growth
         curve

We repeat the Otrees example, replacing the 3 independent univariate Normal priors for each f _ik , k=1,2,3 by a multivariate Normal prior f _i ~ MNV( m , T )

   model {
      for (i in 1:K) {
         for (j in 1:n) {
            Y[i, j] ~ dnorm(eta[i, j], tauC)
            eta[i, j] <- phi[i, 1] / (1 + phi[i, 2] * exp(phi[i, 3] * x[j]))
         }
         phi[i, 1] <- exp(theta[i, 1])
         phi[i, 2] <- exp(theta[i, 2]) - 1
         phi[i, 3] <- -exp(theta[i, 3])
         theta[i, 1:3] ~ dmnorm(mu[1:3], tau[1:3, 1:3])
      }
      mu[1:3] ~ dmnorm(mean[1:3], prec[1:3, 1:3])
      tau[1:3, 1:3] ~ dwish(R[1:3, 1:3], 3)
      sigma2[1:3, 1:3] <- inverse(tau[1:3, 1:3])
      for (i in 1 : 3) {sigma[i] <- sqrt(sigma2[i, i]) }
      tauC ~ dgamma(1.0E-3, 1.0E-3)
      sigmaC <- 1 / sqrt(tauC)
   }


Data ( click to open )

Inits for chain 1        Inits for chain 2    ( click to open )


Results

A 4000 iteration Metropolis adaptive phase plus 1000 update burn in followed by a further 10000 updates gave the parameter estimates: