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    $\begingroup$ In general, it is never the case that the intercept of any GLM (mixed or not) must equal the grand mean of the responses (especially when using a non-linear link). That result generally holds only for ordinary least squares regression. $\endgroup$ Commented Oct 21, 2020 at 15:51
  • $\begingroup$ Thanks for your fast reply, @whuber! I am a bit confused by your answer because Agresti (2013, p.552 ff.) states that the grand mean of nbinom-regression always equals the sample mean (his formulation sounds like a theorem). Although the example he is providing has only one dummy coded predictor. So I thought, if the coefficient for the dummy variable there expresses the difference between the two categories of the predictor so that the intercept is the mean of one of the dummy category this must work for weighted effect coding with the sample grand mean, too. Or is this naive? $\endgroup$ Commented Oct 23, 2020 at 7:05
  • $\begingroup$ Further I found out that if I remove values with residual outliers the mean of the sample and the intercept are closer to each other. But why is this not the case for ordinary least squares regression? $\endgroup$ Commented Oct 23, 2020 at 7:05