Description

In empirical research we often have nested data. Examples of nested data are when we have measurements of children from different classes or schools, measurements of employees in firms, or measurements of members of different organizations such as parties. One important class of nested data is longitudinal data, where there are measurements at different time points nested within an individual.

Nested data create dependent observations, i.e., children in one class are more alike than children from different classes or measurements of one subject are more alike than measurements of different subjects. The statistical analysis needs to take into account this dependency. Two classes of regression models exist that deal with this dependency: the first class, known as repeated measures ANOVA, ignores the dependency when estimating the regression weights but adjusts standard errors to obtain valid inference; the second class includes specific parameters in the regression model that account for the dependency. The latter model is the so-called multilevel regression model (also known as hierarchical model or mixed model). In this course the multilevel regression model will be introduced and explained in much detail. Also attention will be paid to how it can be fitted to data by making use of the R software.

The course consists of the following parts: 

• Presenting the basic multilevel model for cross-sectional hierarchical data
• Multilevel models for cross-classified/multi-membership data (e.g., students are nested into schools but at the same time also into neighborhoods in which they live)
• Inference and assumption checking for multilevel models
• Discussing the multilevel model for longitudinal data

For each part, the theory will be presented and illustration will be discussed in practical exercises in R.

Mode of instruction

• The course will be on campus
• Lectures (theory and illustrative examples in R)
• Practical sessions with exercises in R (students work on the exercises and solutions are discussed at the end)
• Students can use (and should bring) their own laptop with R (and Rstudio) installed
• Students may be asked to do some preparations in advance (e.g., read parts of a book, watch a video, prepare an exercise). Instructions follow in the beginning of January 2025 through email (for those enrolled in the course).

Reading list

• Luke, D. A. (2004). Multilevel Modeling. Sage University Paper Series on Quantitative Applications in the Social Sciences, 07-143. Thousand Oaks, CA: Sage.
• Singer, J. D. and Willett, J. B. (2003). Applied longitudinal data analysis: modeling change and event occurrence. Oxford University Press, Inc. (Chapters 1-8)
• Hox, J. (2010). Multilevel analysis. Techniques and applications (2nd ed.). New York, NY: Routledge. (Chapters 1-6, see https://joophox.net/mlbook2/MLbook.htm)
• Raudenbush, S. W., & Bryk, A. S. (2001). Hierarchical linear models: Applications and data analysis methods (2nd ed.). Thousand Oaks, CA: Sage.
• Roback, P., & Legler, J. (2021). Beyond Multiple Linear Regression. Applied Generalized Linear Models And Multilevel Models in R (1st ed.). Boca Raton, FL, USA: CRC Press. (Chapter 9)

Fees

Target group	One day	Two days	Three days
PhD candidates FSW	FREE	FREE	FREE
Staff FSW	€330	€440	€550
Other Leiden University PhD candidates	€235	€345	€455
Externals	€490	€655	€820

Entry requirements

• Open to PhD students and staff members of the Faculty of Social and Behavioral Sciences, ASCL and ICLON. Also externals can participate in the course.
• Basic knowledge of linear regression (bachelor level) and R required. A list of materials that one can go through to reach the required R level will be made available. A useful reference is https://www.youtube.com/ 
  (MarinStatsLectures - R Tutorials-MarinStatsLectures)