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I am trying to fit accuracy data (taking values 0 or 1) using glmer and I am puzzled to observe that the residuals of the model don't have a null mean. Wasn't this the whole point of the optimization..? Does it mean that the model fails to converge although there was no warning message? I observe the same behavior with simple glm models. My data has very high mean accuracy (.88), could it be part of the problem?

An example model:

final<- glmer(acc ~ group*I(soa/10) + group*I(scale(soa*soa)) + 
            (1 |suj),  family=binomial(link="probit") ,data.f, glmerControl(optimizer="bobyqa", optCtrl = list(maxfun = 150000)))

and here the binned plot for fitted vs residuals

binnedplot(predict(final), resid(final), cex.pts=1, col.int="black")

enter image description here

Thank you very much for your answers.

(A reproducible example can be found here)

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    $\begingroup$ this is probably a Jensen's inequality issue en.wikipedia.org/wiki/Jensen's_inequality ... can we have a (simple) reproducible example please? $\endgroup$
    – Ben Bolker
    May 30, 2016 at 1:38
  • $\begingroup$ e.g. stats.stackexchange.com/questions/162676/… $\endgroup$
    – Ben Bolker
    May 30, 2016 at 1:55
  • $\begingroup$ Thank you very much for your answer Dr Bolker. I'm afraid there is a need for a certain number of data points to observe this strange pattern so I put a dataframe and a minimal script on this drive: drive.google.com/… $\endgroup$
    – Tom Bug
    May 30, 2016 at 11:25
  • $\begingroup$ Do you know if that completely invalidates my model or if I am authorized to draw some conclusions e.g. on the effect of the predictor SOA (considering that the residuals all seem equally biased when plotted against SOA)? $\endgroup$
    – Tom Bug
    May 30, 2016 at 11:36

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