Mixed Models for Discrete Data

Summary

Extends mixed-model machinery from continuous outcomes to binary, count, and ordinal outcomes through the generalized linear mixed model framework, with random effects living on the link-function scale. Develops the critical subject-specific versus population-averaged distinction that arises only with non-linear links, working through the approximate conversion formula and showing why conditional odds ratios are always larger in magnitude than marginal ones. Closes with estimation challenges including Laplace approximation and adaptive Gaussian quadrature, contrasting GLMMs with generalized estimating equations that target the population-averaged effect directly.