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I am trying to use random effects on both the location and scale parameters in a lognormal regression. As you can see in the JAGS code below, I am essentially fitting a accelerated failure time model with interval censored log-normal failure times. I am having problems coming up with decent non-informative priors for the random effects of the scale parameter (for which I use disp in the code). The way I have it set up now is really sensitive to priors specification. Anyone have any suggestions on how to proceed?

With no random effect on the scale parameter and using a $U(0,big)$ on the inverse of the srqt of the scale, the model seems to converge just fine with estimates that make sense.

Eventually I want to add fixed effects to this regression but am simply trying to fit this simpler model at the moment.

model{
      for (i in 1:study){
          for (j in offset[i] : (offset[i+1] - 1) ){
              y[j] ~ dinterval(t[j], lim.s[j,1:2])
              t[j] ~ dlnorm(mu[i],disp[i])
           } 
       } 
     for (j in 1:study){
       beta1[j] ~ dnorm(0,taup)
       mu[j] <- beta0 + beta1[j]
       alpha1[j] ~ dnorm(0,taup.d)
       inv.disp[j] ~ dlnorm(log.inv.disp.hat[j],disp.inv.disp)
       log.inv.disp.hat[j] <- alpha0 + alpha1[j]
       disp[i] <- 1/inv.disp[j]^2
     }

    ## random effects
    alpha0 ~ dnorm(0,0.001)
    beta0 ~ dnorm(0,0.001)

    ## hyperprior on  sqrt(inverse dispersion) for prior on dispersion
    inv.disp.inv.disp ~ dunif(0.01,100)
    disp.inv.disp <- 1/inv.disp.inv.disp^2

    ## hyper prior for beta1
    sigmap ~ dunif(0.01,100) 
    taup <- 1/(sigmap*sigmap)

    ## hyper prior for alpha1 
    sigmap.d ~ dunif(0.01,100)
    taup.d <- 1/(sigmap.d*sigmap.d)
}
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I have had some luck ($N=1$) with the following: Prior distributions for variance parameters in hierarchical models. In the paper, the variances are not themselves hierarchical, but it might provide an alternative starting point. There's also some good information about speeding up MCMC convergence using redundant parameterizations, which may prove useful.

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  • $\begingroup$ Thanks. The parameterization I am using is also from Gelman. I'll give this paper a re-read to see if I get any ideas. $\endgroup$ – scottyaz Feb 26 '12 at 17:49

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