Classical measurement error model...
model {
for (i in 1:N) {
for (j in 1:3) {
y[i,j] ~ dnorm(psi[i,j], inv.sigma.squared)
psi[i,j] <- alpha[i] + beta[i]*(t[i,j] - tbar)
+ gamma*(
mu0 [i] - y0bar)
}
alpha[i] ~ dnorm(mu.alpha, inv.omega.alpha.squared)
beta[i] ~ dnorm(mu.beta, inv.omega.beta.squared)
mu0[i] ~ dnorm(mu.eps, inv.omega.eps.squared)
y0[i] ~ dnorm(mu0[i], inv.sigma.squared)
}
inv.sigma.squared <- 1/sigma.squared
inv.omega.alpha.squared <- 1/omega.alpha.squared
inv.omega.beta.squared <- 1/omega.beta.squared
inv.omega.eps.squared <- 1/omega.eps.squared
sigma.squared <- pow(sigma, 2)
omega.alpha.squared <- pow(omega.alpha, 2)
omega.beta.squared <- pow(omega.beta, 2)
omega.eps.squared <- pow(omega.eps, 2)
log(sigma) <- log.sigma
log.sigma ~ dunif(-10, 10)
omega.alpha ~ dunif(0, 100)
omega.beta ~ dunif(0, 100)
omega.eps ~ dunif(0, 100)
mu.alpha ~ dnorm(0, 0.0001)
mu.beta ~ dnorm(0, 0.0001)
mu.eps ~ dnorm(0, 0.0001)
gamma ~ dnorm(0, 0.0001)

y0bar <- mean(y0[])
}

Inits:
list(log.sigma = 0, omega.alpha = 0.1, omega.beta = 0.1,
mu.alpha = 0, mu.beta = 0, gamma = 0
,
mu.eps = 0, omega.eps = 0.1,
alpha = c(0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0),
beta = c(0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0),
mu0 = c(0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0)
)

Data...

   node   mean   sd   MC error   2.5%   median   97.5%   start   sample
   deviance   1119.0   36.68   1.029   1048.0   1119.0   1193.0   10001   50000
   gamma   1.004   0.1597   0.004629   0.7242   0.9923   1.353   10001   50000
   mu.alpha   6.134   0.1619   0.00212   5.819   6.135   6.453   10001   50000
   mu.beta   -1.064   0.1406   0.005251   -1.336   -1.065   -0.789   10001   50000

Dbar = post.mean of -2logL; Dhat = -2LogL at post.mean of stochastic nodes
   Dbar   Dhat   pD   DIC   
y   815.571   719.083   96.488   912.059   
y0   303.517   250.644   52.873   356.389   
total   1119.090   969.727   149.361   1268.450   

Baseline measurement as a direct covariate...
model {
for (i in 1:N) {
for (j in 1:3) {
y[i,j] ~ dnorm(psi[i,j], inv.sigma.squared)
psi[i,j] <- alpha[i] + beta[i]*(t[i,j] - tbar)
+ gamma*(
y0 [i] - y0bar)
}
alpha[i] ~ dnorm(mu.alpha, inv.omega.alpha.squared)
beta[i] ~ dnorm(mu.beta, inv.omega.beta.squared)
mu0[i] ~ dnorm(mu.eps, inv.omega.eps.squared)
y0[i] ~ dnorm(mu0[i], inv.sigma.squared)
}
inv.sigma.squared <- 1/sigma.squared
inv.omega.alpha.squared <- 1/omega.alpha.squared
inv.omega.beta.squared <- 1/omega.beta.squared
inv.omega.eps.squared <- 1/omega.eps.squared
sigma.squared <- pow(sigma, 2)
omega.alpha.squared <- pow(omega.alpha, 2)
omega.beta.squared <- pow(omega.beta, 2)
omega.eps.squared <- pow(omega.eps, 2)
log(sigma) <- log.sigma
log.sigma ~ dunif(-10, 10)
omega.alpha ~ dunif(0, 100)
omega.beta ~ dunif(0, 100)
omega.eps ~ dunif(0, 100)
mu.alpha ~ dnorm(0, 0.0001)
mu.beta ~ dnorm(0, 0.0001)
mu.eps ~ dnorm(0, 0.0001)
gamma ~ dnorm(0, 0.0001)

y0bar <- mean(y0[])
}

Inits:
list(log.sigma = 0, omega.alpha = 0.1, omega.beta = 0.1,
mu.alpha = 0, mu.beta = 0, gamma = 0,
mu.eps = 0, omega.eps = 0.1,
alpha = c(0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0),
beta = c(0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0),
mu0 = c(0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0))

Data...

   node   mean   sd   MC error   2.5%   median   97.5%   start   sample
   deviance   1115.0   34.94   0.6869   1046.0   1115.0   1184.0   10001   50000
   gamma   0.675   0.08526   0.001505   0.5055   0.6752   0.8403   10001   50000
   mu.alpha   6.137   0.1518   7.699E-4   5.839   6.136   6.434   10001   50000
   mu.beta   -1.056   0.1466   0.006404   -1.339   -1.056   -0.7769   10001   50000
   
Dbar = post.mean of -2logL; Dhat = -2LogL at post.mean of stochastic nodes
   Dbar   Dhat   pD   DIC   
y   814.684   716.752   97.932   912.616   
y0   300.487   226.607   73.879   374.366   
total   1115.170   943.359   171.811   1286.980