Linear Mixed Effects Models

The induced random effects covariance structure can often be described with relatively few parameters, regardless of the number and timing of the measurement occasions. Because linear mixed effects models explicitly distinguish between fixed and random effects, they allow the analysis of between-subject and within-subject sources of variation in the longitudinal responses. This chapter highlights some of the appealing aspects of the linear mixed effects model alluded to earlier. It considers the form of the induced random effects covariance structure for longitudinal data in the more general case. The linear mixed effects model can be motivated by a two-stage random effects formulation of the model. Indeed, some of the main ideas behind the mixed effects model are often better understood by considering the model as arising from a two-stage specification. The chapter provides a non-technical discussion on the prediction of random effects.