A Random Effects Model for Binary Data

This paper presents a method based on maximizing the marginal likelihood for analyzing binary data with random effects. With the assumption of a parametric family that allows for a wide variety of shapes for the distribution of the random effects, the marginal likelihood can be computed without numerical integrations. The method uses local independence models as well as those that incorporate additional dependence among the responses. Two examples, a panel study with binary responses and an analysis of item-response data, will be used to illustrate the method.