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I have a 2 by 2 design with 12 subjects. The two factors are within-subjects variables. For each cell, 24 responses were collected from each subject. My question is whether I need to aggregate every 24 responses into a mean and then use the mean in lmer as the dependent variable. This webpage http://talklab.psy.gla.ac.uk/simgen/faq.html seems to suggest that aggregation is not needed if use mixed effects model, but I doubt that it is true.

Also, if the responses are binary responses, can I just average them and use generalized lmer with binomial family?

Thanks.

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Not only is it not needed, it's wrong. Don't aggregate. You're modelling every data point.

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    $\begingroup$ Thanks. But could you elaborate why? It seems to me that the 24 responses made by the subjects are correlated, and so their residuals should be correlated too. Is this correlation somehow accounted for by the mixed effects model? How? $\endgroup$
    – zywind
    Apr 6, 2012 at 20:50
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    $\begingroup$ That's what the 'random' part of a random effects (aka mixed effects) model does. The individual estimates are correlated and should therefore shrink towards a subject-specific mean. Assuming they come from a subject-specific distribution will make that happen. $\endgroup$ Apr 6, 2012 at 21:03

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