Modelling and generating correlated binary variables

Many applications use simple parametric models for the correlation structur e of binary responses which are observed in clusters. The usual approach, t o use correlation Models appropriate for normally distributed responses, su ffers from two drawbacks when the marginal probabilities within the cluster s differ. First, as it does not explicitly take into account constraints on the second moments which must be satisfied for binary responses, it may fa il to model realistically the range of correlations present in the data. Se condly, computer simulation of observations from these models is very diffi cult. We present an alternative class of correlation models which reflect t he binary nature of the responses and allow for simple simulation.