## Admission requirements

It is recommended that students are familiar with linear and generalized linear models, such as the logistic regression for binary data. Students should also be familiar with matrix algebra and programming in R. This prerequisite knowledge can be acquired from the courses 'Linear and generalized linear models', Linear Algebra and 'Statistical Computing with R'. Thus, it is strongly recommended to have followed these courses first.

## Description

Linear regression models and generalized linear models, such as the logistic regression model for binary data or the log-linear model for count data, are widely used to analyze data in a variety of applications. However, these models are only appropriate for independent data. In many fields of application dependent data may occur. For instance, when individuals belong to the same family or when data are collected repeatedly in time for the same subjects.

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 particular, the course consists of five main sections:

Marginal models

Linear mixed models

Generalized Estimating equations

Missing Data

Generalized Linear Mixed Models.

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.

## Course Objectives

In general, when students are confronted with practical data they 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.

At the end of the course, the MSc student can:

Choose an adequate analysis method for repeatedly measured data considering the limitations of simplistic analysis methods that ignore the correlations in repeatedly measured data.

Use statistical software, e.g., R, to perform an analysis with multivariate models and generalized linear mixed models, using the (Restricted) Maximum Likelihood or Generalized Estimating Equations method.

Draw conclusions using the output from the software in terms of the practical problem.

Choose a suitable estimation procedure for repeated measures data.

Choose in practical applications which variables should be used in the mean or the random part of the model.

Determine a proper strategy for model building.

Evaluate in practical applications, which are the hypotheses of interest, which model parameters are involved in these hypotheses, and which tests are appropriate.

Identify the different mechanisms that generate missing data and which of the discussed methods in this course give valid inference under the different mechanisms.

Evaluate the validity of the model assumptions.

## Timetable

In MyTimetable, you can find all course and programme schedules, allowing you to create your personal timetable. Activities for which you have enrolled via MyStudyMap will automatically appear in your timetable.

Additionally, you can easily link MyTimetable to a calendar app on your phone, and schedule changes will be automatically updated in your calendar. You can also choose to receive email notifications about schedule changes. You can enable notifications in Settings after logging in.

Questions? Watch the video, read the instructions, or contact the ISSC helpdesk.

**Note:** Joint Degree students from Leiden/Delft need to combine information from both the Leiden and Delft MyTimetables to see a complete schedule. This video explains how to do it.

## Mode of instruction

The material will be covered using lectures, quizzes and practical sessions. The course is given in a blended learning style integrating online media as well as traditional face-to-face on campus teaching:

During the lectures the theory will be covered and worked-out examples will be discussed. The lectures will be given mainly with online media combined with quizzes and face-to-face teaching sessions where a short review of the material will be provided followed by questions and discussions on the covered topics.

During the practical sessions, the theory covered will be applied by analysing real datasets. Questions on the online components and the practicals may be posted online on the forum before each face-to-face teaching session.

Lecture notes are leading and worked-out case studies in R are given with solutions for self-study. Some books are suggested (optional) for further details. Study material, including data sets for the case studies mentioned, is available on Brightspace.

About halfway down the course students will start working in groups on case studies that are handed out, under supervision of the teacher. 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.

## Assessment method

A written exam (2/3) with open questions and case study report (1/3). The case study report and the written exam should each be assessed with a minimum grade of 5 to obtain the course credits. The final grade should be at least 5.5 (which will be rounded to 6) to get a pass. Students may take a written re-exam following the university rules. Unless the student decides to follow the course again in a next year, the final grade for the case study is binding. The date for handing in the case study report will be agreed upon during the course.

If the grade of the assignment is lower than 5.5, the assignment can be improved, but the final grade of the assignment cannot become higher than 5.5.

Partial grades cannot be carried over to the next academic year, the grade of the group assignment and the grade of the exam should be obtained within the same year.

## Reading list

The following books are occasionally referred to for further reading, but they are not compulsory reading for the exam.

Fitzmaurice, G., Laird, N., and Ware, J. (2011). Applied Longitudinal Analysis, 2nd Ed. Hoboken: John Wiley & Sons.

Verbeke, G. and Molenberghs, G. (2000). Linear Mixed Models for Longitudinal Data. New York: Springer-Verlag.

Diggle, P., Heagerty, P., Liang, K.-Y., and Zeger, S. (2002). Analysis of Longitudinal Data, 2nd edition. New York: Oxford University Press.

Faraway (2006). Extending the linear model with R. generalized linear, mixed effects and nonparametric regression models. Chapman & Hall/CRC.

McCulloch, Searle & Neuhaus (2008) Generalized, linear and mixed models. Wiley Blackwell.

The first two books are indicative for the applied level of this course. The third and fifth books are more technical and intended as reference. The Faraway book is relevant for the course about linear and generalized linear models, as well. These books are occasionally referred to for further reading, but they are not compulsory reading for the exam.

## Registration

As a student, you are responsible for enrolling on time through MyStudyMap.

In this short video, you can see step-by-step how to enrol for courses in MyStudyMap.

Extensive information about the operation of MyStudyMap can be found here.

There are two enrolment periods per year:

Enrolment for the fall opens in July

Enrolment for the spring opens in December

See this page for more information about deadlines and enrolling for courses and exams.

**Note:**

It is mandatory to enrol for all activities of a course that you are going to follow.

Your enrolment is only complete when you submit your course planning in the ‘Ready for enrolment’ tab by clicking ‘Send’.

Not being enrolled for an exam/resit means that you are not allowed to participate in the exam/resit.

## Contact

s.tsonaka@lumc.nl

## Remarks

**Software**

Starting from the 2024/2025 academic year, the Faculty of Science will use the software distribution platform Academic Software. Through this platform, you can access the software needed for specific courses in your studies. For some software, your laptop must meet certain system requirements, which will be specified with the software. It is important to install the software before the start of the course. More information about the laptop requirements can be found on the student website.