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I have fitted a 3-level cross-classified model using MCMC with 5000 burn-in and 50,000 chain. I have used runmlwin and mcmcsum to examine the MCMC chain. Due to auto-correlation the reported effective sample size is only 1961. The Raftery-Lewis value (for 2.5 percentile) is 19445. Does this Raftery-Lewis value tell me that I need at least 19,445 iterations or 19,445 effective (independent) iterations? In other words, is the Raftery-Lewis value telling me I need to run the chain long enough such that the effective sample size is 19,445?

Thank you for your time
Rach

Hi Rach,
Raftery and Lewis is a completely different diagnostic to the ESS and so works on actual iterations and so you need to run for 19,445 actual iterations to satisfy it. With regard ESS generally one looks for some criterion like > 500 for all parameters. The ESS works on correlations in the chains whilst the Raftery-Lewis looks at behaviour around the quantiles.
Hope that helps,
Bill.

Thank you Bill - very helpful.