Mixed and longitudinal modeling
|Period:||Semester 2, Block III, IV|
- Yes Elective choice
- Yes Contractonderwijs
- Yes Exchange
- Yes Study Abroad
- No Evening course
- Yes A la Carte
- No Honours Class
It is recommended that students are familiar with linear models, e.g. regression and analysis of variance, and generalized linear models, e.g. logistic regression for binary data. Students should also be familiar with matrix and vector algebra. Within this master this pre-knowledge can be aquired from the courses 'Mathematics for statisticians' and 'Linear and generalized linear models', and it is recommended that students follow these courses first.
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.
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, includi