ABSTRACT
This chapter explores the generalized linear model (GLM) has been extended to deal with longitudinal data in two different ways, marginal models and conditional or generalized linear mixed effects models. Marginal models are used to make inferences about population means on some transformed scale, for example, the logit or log scale, by modeling the mean conditional on the covariates but not on unobserved random effects. In generalized linear mixed effects models, by contrast, random effects are used to model heterogeneity in some of the regression coefficients but conditional on these random effects the repeated measurements for an individual are independent. The problem with applying a direct analogue of the GLM to longitudinal data with non-normal responses is that there is usually no suitable likelihood function with the required combination of the appropriate link function, error distribution, and correlation structure to allow maximum likelihood to be used.
