The linear model, e.g. analysis of variance or linear regression, and the generalized linear model, e.g. logistic regression for binary data or log linear models for count data, are widely used to analyse data in a variety of applications. However, these models are only appropriate for independent data, e.g. data considered as randomly sampled from some population. In many fields of application dependent data may occur. For instance, because observed animals are housed in the same pen, fertility trends create dependence between plants at close distance, individuals are from the same family or data are collected repeatedly in time for the same subjects or individuals.
Introduction of random effects in the linear or generalized linear model is a simple and constructive expedient to generate feasible dependence structures. The extended classes of models are referred to as linear mixed models (LMMs) and generalized linear mixed models (GLMMs). The use of such models is the subject of this course. Competing models, where dependence is not modeled by introduction of extra random effects, will be discussed as well. Part of this course will focus upon analysis of repeated measurements or longitudinal data.
Inferential techniques comprise restricted (or residual) maximum likelihood (REML), a modified version of maximum likelihood, but also generalized estimation equations (GEE) that requires less strenuous model assumptions.
In this course, emphasis will be on gaining an understanding of the models and the kind of data that can be analysed with these models. Different inferential techniques will be discussed, but without undue emphasis on mathematical rigor. Students, when confronted with practical data should be able (1) to decide whether there is a need to model dependence between the data, (2) to decide upon a model with an appropriate dependence structure and (3) to perform a proper analysis.
The course will consist of a two-hour lecture and a two-hour practical per week, for 14 weeks. In week five, students will be asked to analyse a practical data set, and hand in a report in week seven. There will be a written exam at the end of the course. Assessment of a student will be based on the case study report (1/3) and the written exam (2/3), with a minimum grade of 5 for the latter.
Literature – Faraway (2006), Extending the linear model with R: generalized linear, mixed effects and nonparametric regression models. Chapman & Hall/CRC. – Fitzmaurice, Laird & Ware (2004). Applied longitudinal analysis. John Wiley & Sons. – McCulloch, Searle & Neuhaus (2008) Generalized, linear and mixed models. Wiley Blackwell.
Comment
The first two books are indicative for the applied level of this course. The third book is more technical and intended as a reference book. The books by Faraway and by McCulloch, Searle & Neuhaus are relevant for the course about linear and generalized linear models as well.