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 2013-14 under the tab “Masters Programme” at http://www.math.leidenuniv.nl/statscience
Mode of Instruction
The course will consist of two two-hour lectures and a two two-hour practicals per week, for 7 weeks. In week five, students will be asked to analyze a practical data set, and hand in a report in week seven.
A written exam (2/3), case study report (1/3) and presentation (pass / fail)
The case study report 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.
The date of the written exam is scheduled for the 3rd of April 2014 from 14.00 to 17.00 (room is tba), the resit is scheduled for July 1, 2014 from 10.00 to 13.00 hours (room is tba).
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.
Besides the registration for the (re-)exam in uSis, course registration via blackboard is compulsory.
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.