ABSTRACT
Methods for analyzing correlated binary data have been well established in recent decades. Pendergast et al. (1992) offer a review of methods for correlated binary data, with a focus on cluster-correlated observations. Some of these methods, including marginal, random effects, and Markovian or conditional models, have been introduced in Chapter 4 and studied in subsequent chapters. However, the justification of inferences that rely on such methods usually rests upon the approximate normality of the statistics of interest. Such a distributional assumption may be untenable when samples are small or sparse. If a normal approximation is not accurate, the result might be tests that do not preserve the a priori testing level established by the investigator. Likewise, actual coverage probabilities for confidence intervals may be much lower or higher than the nominal confidence level. Moreover, where likelihood or quasi-likelihood methods are applied, inference can be further complicated when parameter estimates lie at or near the boundary of the parameter space. The following two examples illustrate these perils of approximate unconditional inference for cluster-correlated binary data. In this chapter, we will use the examples introduced in Sections 2.7 and 2.8.
