MCMC convergance failing for bayesmh

[Erik Drysdale]

Hi there,

I am trying to estimate a random effects model for logistic regression with bayesmh. I have repeated measurements for respondents, with 11 covariates measured for each response (see Data.png for an idea of what the data looks like). I'm trying to estimate a RE effects model with the following specification:

bayesmh y U0[record] U1[record]#c.feature1 ... U11[record]#c.feature11, likelihood(logit) priors(....)

Where every respondent has their own RE coefficient for each covariate. When I assign independent priors for each parameter, the MCMC model converges appropriately.

--- Works fine ---
for i=[1,...12]
prior({U[i]), normal(0, 4))

However, when I try to assign a hyperpriors on each mean, then MCMC no longer converges. Specifically:


--- Fails to converge ---
prior({U1 ... U11}, mvnormal(11, {mu1}, ..., {mu11}, 1)
prior({mu[i]}, N(0,4))

Specifically, there are three ways in which the posterior distribution does not appear to be converging:

1. The are multiple equilibria across the chains (see fig1.png): i.e. the posterior is multi-modal across the chains.
2. Within a single chain, the posterior does not appear to be stationary (see fig2.png).
3. There is high auto-correlation even after 40 lags with a thinnning of 2 (see fig3.png).

Note that I am using 10K burn in iterations, 10K iterations after that, and a thinning of 2 (i.e. discarding every other observation).

Any advice on what to do when a Bayesian model does not appear to be converging in its posterior distribution across or within chains? Do I need to manually tune the MCMC parameters?

Any suggestions would be welcome,
Thanks, Erik