Suspiciously high Multivariate PSRF from gelman.diag() I am using "Multivariate PSRF" statistics from gelman.diag() function to analyze my MCMC chains. Now I analyzed convergence 471 variables (parameters for each site). 


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*How is it possible that "Multivariate PSRF" says 1.248096, when psrf for each of 471 sites ranges from 0.9996 to 1.012 max? Psrf CI is 1.044 max! 

*It seems Multivariate PSRF grows with the number of variables, which is definitely not desired of convergence assessment.


I think I can safely say that the model converged, but the Multivariate PSRF suggests otherwise... so is it computed wrong or something?
 A: This is just a multiple comparisons problem. The multivariate PSRF is derived from the linear combination of variables that has the maximum scalar PSRF. With 471 variables, there is a good chance to find an "optimal" linear combination that has high PSRF just due to random fluctuations in the data.
You should feel free to ignore it in this case
A: As Martyn says, I would not be too worried about the MPSRF in this case. I don't think that it is being computed incorrectly, but it occasionally gives false positives and false negatives.  This is true of all convergence criteria, which is why it is important to always visualise trace plots (at least) for all key parameters in your model (NOT just the ones that you are interested in).  For example, consider the following:
  library(coda)
  set.seed(1)
  chain1 <- mcmc(rnorm(100, 1:100, 10))
  chain2 <- mcmc(rnorm(100, 100:1, 10))

  gelman.diag(mcmc.list(chain1, chain2), autoburnin=FALSE)
  lattice::xyplot(mcmc.list(chain1, chain2), autoburinin=FALSE)


This is obviously a pathological example, but it illustrates my point :)
Matt
