

Estimated probabilities in 2level lo... 

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Dear Prof. Muthen, I'm running a twolevel logistic regression and was wondering if the correct way to estimate probabilities is: 1) simply plug in the coefficient estimates and the estimated random effects 2) averaging over the distribution of the random effect ("empirical bayes probabilities") Or both are correct but simply different ways to estimate probabilities? If so when/why I have to choose between the two? Can you suggest me some readings on this topic? Many thanks. 


You would integrate over the random effect distribution, so use 2). This gives you P(u=1). You might also want say P(u=1alpha) with alpha being the mean of the random effect. More on this in e.g.: Fitzmaurice, G.M., Laird, N.M. & Ware, J.H. (2004). Applied longitudinal analysis. New York: Wiley. 

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