How to interpret estimates and correlation of group effects (intercepts and slope) in a mixed-effects model in brms?

Sorry, not really. (this is probably a typo, but not I am speaking about “predictions” not “predictors”). It IMHO tends to be quite dependent on the actual scientific question you are asking. But the general approach is to use posterior_predict or posterior_linpred for some inputs of interest and interpret the results. The plus side is that this automatically incorporates any possible correlations in the posterior.

For example, you may want to plot how the outcome changes as you change a continuous variable and a discrete variable at the same time as in this plot:


The color indicates two groups that are allowed to have different slopes, each line is a sample from the posterior distribution (the response is non-linear here, hence the curved lines), the thick blue stair-like line is what would be expected if there was perfect alignment between doctors and certain guidelines.

We can interpret this as a) there is a disagreement between doctors and guidelines, b) we are less certain about the blue group (because there is less data for them) and c) the groups heavily overlap, so we cannot prove a difference, but we also cannot prove that they are similar as some of the blue curves are very different from the red curves (which have more data and are better constrained)

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