In this paper, we consider latent variable models with random effects to analyze exchangeable binary data with random cluster sizes. Based on this procedure, we can obtain the approximate likelihood estimates of exchangeable binary data by using MC method. Then we can make further inference on the exchangeable binary data based on likelihood procedure. For example, we can select an appropriate model to fit the exchangeable binary data by using AIC and BIC. Theoretical results are obtained establishing the large sample properties of the parameter estimates. An application is made to a data set from a developmental toxicity study. Simulation results further show that our method is valid.