We propose a straightforward approach for simulation of discrete random variables with overdispersion, specified marginal means, and product correlations that are plausible for longitudinal data with equal, or unequal, temporal spacings. The method stems from results we prove for variables with first-order antedependence and linearity of the conditional expectations. The proposed approach will be especially useful for assessment of methods such as generalized estimating equations, which specify separate models for the marginal means and correlation structure of measurements on a subject.
Guerra, Matthew and Shults, Justine, "On the Simulation of Longitudinal Discrete Data with Specified Marginal Means and First-Order Antedependence" (January 2013). UPenn Biostatistics Working Papers. Working Paper 35.