ng the use of broken degrees of freedom in some pairwise comparisons.
- Be aware of the issues involved in representation of blocks by fixed or random effects in the analysis of data collected according to e.g. a block design when data are unbalanced (recovery of inter-block information).
- Be able to motivate the use of restricted maximum likelihood (REML) for unbalanced data.
- Know about the relationship between the ANOVA method and REML for balanced data.
- Be able to decide what kind of test is required for testing fixed effects (Kenward & Roger Approximate F-test) or dispersion parameters (likelihood ratio test) for unbalanced data.
- Be aware of possible boundary problems and remedies in testing dispersion parameters with the likelihood ratio test.
- Have an understanding of BLUEs, BLUPs and the mixed model equations (MME). Understand the difference between the normal equations and MMEs when effects of a factor are either introduced as fixed or as random effects in the model.
- Be aware of the differences between conditional and marginal means in a GLMM. In particular be aware of shrinkage for binary data and a shift for count data in deriving marginal means.
- Be able to decide whether the mean or mode is the proper measure for location in a GLMM for a particular practical problem.
- Be able to motivate penalized quasi-likelihood (PQL) for a GLMM by iterated reweighted REML.
- Be able to broadly explain the pros and cons of a population averaged approach versus a subject specific approach in modelling dependent discrete data.
After the second part of this course a student should:
- Be able to identify which of the methods presented can be used for the analysis of longitudinal normal and non-normal distributed measurements.
- Be able to identify which of the methods are appropriate in studies with unbalanced measurements, long follow-up times or missing data.
- Be able, in the presence of missing data, to identify the different mechanisms that generate missing data and which of the discussed methods in this course give valid inference under the different mechanisms.
- Be able to identify which are the hypotheses of interest, which model parameters are involved in these hypotheses, and which tests are appropriate?
- Be able to decide upon a proper strategy for model building and
- Be able to validate model assumptions.
- Be able to use software, e.g. R, to perform an analysis with an LMM or GLMM, by the ANOVA method, ML, REML, or GEE.
- Be able to interpret output from the software in terms of the practical problem.
- Know the strengths and limitations of various procedures for statistical inference with a mixed model.
For the course days, course location and class hours check the Time Table under the tab “StatSci Students -> Program Schedule” at http://www.math.leidenuniv.nl/statisticalscience
Mode of Instruction
The course will consist of a mix of lectures and practicals. Students will discuss some practical case studies in groups in class with respect to choice of model and aspects of statistical inference. PowerPoint presentations are leading and notes are supplied that provide details, worked case studies, R programs and output, and exercises with solutions for self-study. Some books are suggested (optional) for further details. Study material, including data setsfor the case studies mentioned, is available from Blackboard.
About halfway down the second part of the course (the part about longitudinal data) students will start working in groups on case studies that are handed out, under supervision of the teachers. Each group of students will hand in a written report about their case study. This report will be graded and together with the grade of the written exam determines the final grade of an individual student. Before a group of students hand in their final report, they will present the results of their case study in a plenary session, and be able to use feedback from the other students and teachers to improve upon the report.
A written exam (2/3) with open questions, presentation of the case study and cas