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.

At the end of the course, the student will:

• understand the difference between fixed and random effects;
• know when to apply a mixed model in practice;
• know the most commonly used methods for checking model appropriateness and model fit;
• be able to perform mixed model analyses using statistical software (R, SPSS);
• be able to interpret the output of mixed model analyses in terms of the context of the research question(s);
• be able to report the results of mixed model analyses to non-statistical investigators.

Introduction to Statistics, Classical Methods in Data Analysis, Modern Methods in Data Analysis, or their equivalents.

Participants are expected to be already familiar with the use of R.

Daily quizzes (individual) and a case presentation
All elements have to be awarded with at least a 5.5 in order to pass the final Assessment.