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 analyze 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 require 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 analyzed 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.
For the course days, course location and class hours check the Time Table under the tab “Masters Programme” at http://www.math.leidenuniv.nl/statscience
Mode of Instruction
The course will consist of a mix of lectures and practicals, two days of four hours each per week, for 7 weeks. Students will work in groups on a case study. Students will receive the case study in week 4 and will be asked to hand in a report after week 7.
A written exam (2/3), presentation of the case study and case study report (1/3) (pass / fail).
The case study report and the written exam should be assessed with a minimum grade of 5 to obtain the course credits. The date for the oral presentation of the report and handing in the study report will be agreed upon in the course.
Date information about the exam and resit can be found in the Time Table pdf document under the tab “Masters Programme” at http://www.math.leidenuniv.nl/statscience. The exams take place in the Snellius building, the room will be announced on the electronic billboard, to be found at the opposite of the entrance, the content can also be viewed online at:“http://info.liacs.nl/math/”:http://info.liacs.nl/math/
If the exam does not take place in the Snellius building, then an announcement will be sent via blackboard
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.
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 Faraway book is relevant for the course about linear and generalized linear models as well. These books are occasionally referred to for further reading, but they are not compulsory reading for the exam.
Enroll in Blackboard for the course materials and course updates.
To be able to obtain a grade and the ECTS for the course, sign up for the (re-)exam in uSis ten calendar days before the actual (re-)exam will take place. Note, the student is expected to participate actively in all activities of the program and therefore uses and registers for the first exam opportunity.
Exchange and Study Abroad students, please see the Prospective students website for information on how to apply.
bas [dot] engel [at] wur [dot] nl
- This is a compulsory course in the Master’s programme of the specialisation Statistical Science for the Life & Behavioural sciences.