The variance component estimates in Models 6 and 7, fitted using Bayesian methods, are on the whole smaller than those obtained by pseudo-likelihood (Models
4 and 5). However, they are taken as medians of their posterior distributions and are also based on using a prior that is constrained to be positive (pseudo-likelihood is equivalent to using flat priors). For these reasons they cannot be compared directly. The treatment standard errors in Model 7 are still noticeably increased over those in Model 6 despite the fact that the centre-treatment variance component median is small. It is difficult to decide whether the pseudo-likelihood or Bayesian models are preferable for this example. On the whole, however, the results are very similar.
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