EE) 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.
Broadly, 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 first part of the course is about the linear mixed model (LMM) and the generalized linear mixed model (GLMM). Broadly, the LMM is about analysis of dependent continuous data (assumed to be normally distributed), and the GLMM is about analysis of dependent discrete data (0-1 data, proportions and percentages, counts). Longitudinal data (temporal data, repeated measurements) are discussed in the second part of this course. This is about data where units are repeatedly measured in time, e.g. patients that repeatedly visit a health care centre where relevant variables are measured. Below are more detailed goals for each of the two parts of this course.
After the first part of this course a student should:
- Be able to identify, for a practical problem, which factors and variables should be in the model and whether they should be represented by fixed or random effects.
- Be able to interpret fixed and random effects in terms of population means and dependence structures.
- Be able to explain in general terms how expected mean squares are used for estimation of components of variance and construction of F-tests with the ANOVA method for balanced data.
- Have a global understanding, through the ANOVA method for balanced data, how different random main effects and interactions in the model affect inference about fixed effects, and what their implications are for model selection.
- In particular be aware of the ins and outs of the analysis of a split-plot model for balanced data, including 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 thi