Conditional and Marginal Models
for Binary Mixed Models
Mixed models for
binary data are useful tools for addressing inter-subject heterogeneity and
accounting for clustering or longitudinal correlation. Unlike linear models,
the non-linearity of link functions used for binary data force a distinction
between marginal and conditional interpretations. In this talk, we discuss the
relationships between conditional and marginal link functions for binary mixed
models. This relationship is most apparent in probit
models with a random intercept, as both the conditional and marginal link
functions are probits. We utilize this relationship
to give simple strategies for obtaining desired marginal link functions. Moreover, we develop a general class of
distributions that possess the property of having the marginal and conditional
link functions being associated with the same family of distributions. The
resulting flexible family of models is demonstrated to be related to several
others in the literature and can be used to synthesize many seemingly disparate
modeling approaches. In addition, this family of models offers considerable
computational benefits.