When I fit relatively simple models with MCMCglmm, MCMC sampling usually shows good mixing, or at least if there is some extent of autocorrelation, it is usually easly resolved by specifying priors with a bit more care. However, in some cases - especially when fitting categorical models - MCMC chains look terribly, and no matter how I specify the priors, the chains remain ugly and the effective sample size is embarrasingly low.

Nevertheless, in some cases this seems to be solved, by simply fixing residual variance at an arbitrary number (usually to 1). My questions are:

  • Why does fixing residual variance solve autocorrelation and poor mixing in the MCMC chains?
  • What does residual variance really stand for in the case of Bayesian regressions? I mean, are they functionally the same as in frequentist regression models?
  • What does fixing resudial variance really mean for the model I'm fitting (in terms of reliability, validity, etc.)?

So far as I can see, it is really hard for non-statisticians to educate themselves about how MCMCglmm works, as lots of the information is too technical, and in most cases, mining informations from forums or mailing lists do not provide full answers.

Any help would be appreciated!




With categorical response models, there might not be enough degrees of freedom to fit the variance components of an unconstrained residual covariance matrix, and even if you have, the fit is likely to be poor, which usually means more computation time and less reliability. Besides, such parameters are often not interesting. By fixing the residual variance, MCMC chains no longer have to explore the space in the residual variance parameter dimension, and can focus on the really interesting parameters.

Yes, it's the same concept as in frequentist models.

It probably won't change much the results.

Having a look at Hadfield's discussion on fixing residual variances (from page 49) might be of use.


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