Description

In empirical research we often have nested data. Examples of nested data are when we have measurements of children from different classes or school, measurements of employees in firms, or measurements of members of different organisations 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.

Programme

In this course we will deal with more advanced multilevel modeling topics:

1. First, we will discuss generalized multilevel models which can be used when the dependent variable is not continuous but, for example, binary (logistic multilevel regression).
2. Second, we will also discuss non-linear multilevel models. For example, polynomial (curvilinear, cubic, …) growth models.
3. Third, more complex hierarchical data structures will be touched upon, like multiple membership models (a student having multiple teachers) and three level models (students nested in classes nested in schools).
4. Finally, we will very briefly sketch further modeling possibilities, like time-series analysis (VAR, ARIMA) and SEM.
    

Course objectives

• Be able to distinguish between advanced types of nested data (multiple memberships and three level data);
• Knowing how to deal with non-linear relations and the dependent variable not being continuous; and
• Learn R software for fitting the multilevel models.
   

Entry requirements

• Basic knowledge of of multilevel modeling (basic course) and R required
  • a list of materials that one can go through to reach the required R level can be obtained upon request from the coordinator. 

Mode of instruction

• 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 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 first week of January 2022 through email (for those enrolled in the course, see further).

Recommended 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 6 & 9)
• Raudenbush, S. W., & Bryk, A. S. (2001). Hierarchical linear models: Applications and data analysis methods (2nd ed.). Thousand Oaks, CA: Sage.

Fees

Target group	One day	Two days	Three days
PhD candidates FSW	FREE	FREE	FREE
Staff FSW	€300	€400	€500
Other Leiden University PhD candidates	€215	€315	€415
Externals	€450	€600	€750