I am simulating a hierarchical model with MCMC Bayesian methods. The model has three groups of individual effects modelled as random effects drawn from normal priors with mean zero and variances estimated from the data. The priors for variances are inverse gamma with different hyperparameters to assess sensitivity. The posterior distributions of random effects are not showing convergence properly, but the 3 chains run in parallel from different starting values move towards close points and then stay there. This is an example where burnin is kept: enter image description here

Since "fixed" parameters in the model are converging properly, my question is to what extend this behavior of random effects can be due to a poor prior for their variance. I understand that Gelman (2006) advises against the inverse gamma prior, because IG(0.001,0.001) would results in improper posteriors, while other hyperparameters would be informative and produce results sensitive to specific values. My attempt with informative inverse gamma priors is a starting point to make the model work and then to see whether we can move to non-informative priors. Hence I would have expected convergence, even if with posteriors sensitive to IG hyperparameters.

Can the lack of convergence for random effects as in the trace plot above be due to a poor informative prior on variances?

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    $\begingroup$ It is not clear to me what you show in the picture. Can you write the model so we can understand your problem? This seems an identification problem, but without the model I cannot tell $\endgroup$ – niandra82 May 7 '18 at 16:31
  • $\begingroup$ In the picture I show the trace plot and the relative density of one individual among the random effects. I am aware that lack of convergence can be due to identification issues and revising the model would actually be my following step. It would be too long to insert this discussion in this post, though. The question was limited to the possibility that such a behavior of trace plots of random effect can be due to a poor prior on their variance, provided general identification is valid. $\endgroup$ – Jim Conrad May 7 '18 at 18:36
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    $\begingroup$ No, in my opinion/experience it is really difficult that a prior can give this problem. A trace plot like this is due to identification problems. If yours is a mixture type model, than this is due to the label switching. Without the model i cannot help. $\endgroup$ – niandra82 May 7 '18 at 22:08

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