Data obtained describing terrorist events are particularly difficult to analyze, due to the many problems associated with the both the data collection process, the inherent variability in the data itself, and the usually poor level of measurement coming from observing political actors that seek not to provide reliable data on their activities. Thus, there is a need for sophisticated modeling to obtain reasonable inferences from these data. Here we develop a logistic random effects specification using a Dirichlet process to model the random effects. We first look at how such a model can best be implemented, and then we use the model to analyze terrorism data. We see that the richer Dirichlet process random effects model, as compared to a normal random effects model, is able to remove more of the underlying variability from the data, uncovering latent information that would not otherwise have been revealed.