Modelling and generating correlated binary variables

TLDR: This work presents an alternative class of correlation models which reflect the binary nature of the responses and allow for simple simulation of observations from these models.

Abstract: SUMMARY Many applications use simple parametric models for the correlation structure of binary responses which are observed in clusters. The usual approach, to use correlation models appropriate for normally distributed responses, suffers from two drawbacks when the marginal probabilities within the clusters differ. First, as it does not explicitly take into account constraints on the second moments which must be satisfied for binary responses, it may fail to model realistically the range of correlations present in the data. Secondly, computer simulation of observations from these models is very difficult. We present an alternative class of correlation models which reflect the binary nature of the responses and allow for simple simulation. Some key wor-ds: Binary variable; Computer simulation; Correlation structure; Generalised estimating equation.