In the biosciences, response variables are often observed more than once per individual. This enables the researcher to study the development of the variable of interest within individuals, thereby eliminating the variation among individuals, and thus increasing the power of the design. However, since observations on the same individual are almost always correlated, special methods are needed to deal with this dependence.
Another way in which data can be dependent is when there is a hierarchical (multilevel) structure in your data, e.g. patients within hospitals, horses within farms, pupils within classrooms, etc.
Mixed models are one way of analyzing this kind of data. This statistical technique allows for the dependency of measurements in hierarchically structured data, and separately examines the effects of variables at different levels. An important part of the course will be about the use (and theory) of linear mixed effects models (LME’s).
Starting with analysis of summary statistics on each individual's observations, this course will lead you to more advanced methods for analyzing multilevel and longitudinal data. Similarities between longitudinal data analysis and multilevel analysis will be clarified. The course will focus primarily on continuous outcome variables, but attention will also be paid to dichotomous and count data.
The theory will be presented during lectures; computer lab sessions using SPSS and R will give you the opportunity to practice your skills on real data sets.
By the end of the course, you will be able to:
- understand the difference between fixed and random effects
- know when to apply a mixed model in practice
- perform mixed model analyses using statistical software (R, SPSS)
- interpret the output of mixed model analyses in terms of the context of the research question(s)
- know the most commonly used methods for checking model appropriateness and model fit
- report the results of mixed model analyses to non-statistical investigators
Introduction to multilevel modelling
Students will be introduced to mixed and multi-level models, starting with random and fixed effects in a two-level model. The reason for applying mixed models will be explained, and students will apply their first mixed model in R.
Longitudinal data (modelling time)
Students are introduced to the characteristics of longitudinal data, e.g. how repeated measures for the same subject over time are correlated. The students will learn why it is important to take the correlation over time into account. Longitudinal data will be modeled as multi-level data (modeling time); correlation structures in longitudinal data are discussed.
Technical issues in multilevel/longitudinal modelling
Students learn (and apply) the methods for model reduction/selection/ testing and REML estimation in linear mixed models (LMM). Students are also introduced to checking model assumptions / model diagnostics in LMM. Centering explanatory variables and adding polynomial terms to the model will be discussed and are consequently applied by the student in R.
Beyond the Linear Mixed Model
Students are introduced to multi-level models for binomial, Poisson and survival outcomes. Different estimation procedures used by software to apply mixed models are touched upon.
- Introduction to multilevel modelling
The whole course will take place online. The following learning methods will be used:
- Web lectures
- Online discussion forums
- Individual and group assignments
To successfully complete this course, you need to actively participate in the discussion forums and complete the learning unit assignments, including:
- Individual and group assignments
- The completion of a quiz at the end of the first four learning units
- A final assignment: this will be a presentation of a case study by the student. The submission deadline and the date for the redo session will be announced as soon as possible.
As this is a university course, it is covered by academic accreditation. Upon succesful completion of this course, you will receive a recognized certificate from Utrecht University.
To enroll in this course, you need:
- A BSc degree
- Basic programming experience in R, e.g. the ability to read in data and run a simple linear model
- To have followed at least one course in basic statistical methods up to and including simple and multiple linear regression
- Familiarity with likelihood methods (Wald, score and likelihood ratio tests) will facilitate understanding of the theoretical background.
As Mixed Models is an online course, you do need access to an internet connection in order to be able to follow lectures, complete assignments and communicate with fellow participants.