Dear all,


I have a data set with 25 subjects, all with 20 binary responses (psychological learning task). Many subjects gave the 1 response (lets call this response A and the 0 response B) throughout the task.

My goal is to estimate the Probability of A (P(A)), and if it is above chance (the latter is trivial in this data set, but I have several other similar sets where its more of an issue).

If I calculate the proportion of A responses for each subject (mean, na.rm=T), the sample mean is 0.757 (the sample distribution of proportion A is very skewed toward 1, with a few all 0 respondents).

If i instead use glmer: glmer(RespondA~1+(1|Subject),family=binomial,data=data),
Fixed effects:
      Estimate Std. Error z value Pr(>|z|)
(Intercept)    3.660      1.143   3.201  0.00137 **

,with an estimate that is far above 0.757. Plogis(3.66) = 0.974. This estimate is close to the sample median (md =1), but does it make sense?

Ordinary glm, ignoring the Subject factor, gives an intercept closer to the sample mean :

Coefficients:
            Estimate Std. Error z value Pr(>|z|)
(Intercept)   1.1995     0.1073   11.18   <2e-16 ***

(plogis(1.1995) = 0.768)


Can someone please illuminate whats happening here? Is it shrinkage in the GLMM? Seem a bit much for just the intercept right? Overdispersion (dont know much about that...)

kind regards
Björn


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