A well-established approach to modeling clustered data introduces random effects in the model of interest. Mixed-effects logistic regression models can be used to predict discrete outcome variables when observations are correlated. An extension of the mixed-effects logistic regression model is presented in which the dependent variable is a latent class variable. This method makes it possible to deal simultaneously with the problems of correlated observations and measurement error in the dependent variable. As is shown, maximum likelihood estimation is feasible by means of an EM algorithm with an E step that makes use of the special structure of the likelihood function. The new model is illustrated with an example from organizational psychology.