A simple approach for generating correlated binary variates^∗

^∗The views expressed in this article are those of the authors and not necessarily of the FDA

Abstract

Correlated binary data arise frequently in medical as well as other scientific disciplines; and statistical methods, such as generalized estimating equation (GEE), have been widely used for their analysis. The need for simulating correlated binary variates arises for evaluating small sample properties of the GEE estimators when modeling such data. Also, one might generate such data to simulate and study biological phenomena such as tooth decay or periodontal disease. This article introduces a simple method for generating pairs of correlated binary data. A simple algorithm is also provided for generating an arbitrary dimensional random vector of non-negatively correlated binary variates. The method relies on the idea that correlations among the random variables arise as a result of their sharing some common components that induce such correlations. It then uses some properties of the binary variates to represent each variate in terms of these common components in addition to its own elements. Unlike most previous approaches that require solving nonlinear equations or use some distributional properties of other random variables, this method uses only some properties of the binary variate. As no intermediate random variables are required for generating the binary variates, the proposed method is shown to be faster than the other methods. To verify this claim, we compare the computational efficiency of the proposed method with those of other procedures.

Keywords:

• Correlated binary variates
• Correlated poisson variates
• Simulation

^∗The views expressed in this article are those of the authors and not necessarily of the FDA

^∗The views expressed in this article are those of the authors and not necessarily of the FDA

Notes

^∗The views expressed in this article are those of the authors and not necessarily of the FDA