D01-04AM: Multilevel Modeling

After a short review of regression basics, the course discusses modelling heterogeneity and delves into interaction models and fixed versus random effects (our most basic multilevel models). We then build on these basics to construct more complex two-level models, learn about model assumptions and how to deal with violations thereof, and discuss improving the models and model presentation. The last two days then discuss extending what we learned so far to specific data situations such as longitudinal data, or when we have limited dependent variables (e.g., categorical, ordinal).

The course is designed to provide participants with a basic understanding of multilevel models, aka hierarchical models or mixed models. At the end of the course, the students will have a basic conceptual understanding of multilevel models, when to use them, and how to implement them in R. Students will be able to critically assess the appropriateness of such techniques in their own and other people’s research. Each day has a theoretical and a practical component (1.5 hours each). Please bring your own laptop to class with R installed. A basic level of R and an understanding of multiple linear regression are prerequisites for this course. The course will not cover the estimation theory behind multilevel models, so advanced mathematical knowledge or any knowledge of estimation theory is not required.

The course will build on a regression foundation. On day one, we will briefly review the basics of regression and then start a discussion of how to deal with heterogeneity (i.e. if there are reasons to expect that different subgroups in the data exhibit different effects). We will discuss interaction models and the use of fixed effects models, and the conditions under which multilevel modelling (also random effects model) is and is not more appropriate. 

In the second class, we will start with a discussion of nesting and different potential multilevel structures of the data, along with the appropriate statistical notation. Then we will focus on the most basic two-level model (random intercepts) and discuss the assumptions the model makes, and how we can test them. We will also discuss shrinkage, the costs and benefits of hierarchical models, and the conditions needed to run these models. 

On day three we will continue our discussion of two-level models and expand the basic multilevel models to include random slopes. We will cover issues related to sample size and possible solutions for assumption violations in this realm. Then we will make these models more complex by adding multiple random slopes to a single model. The discussion will also focus on data cantering, interaction terms, and plotting. 

On the fourth day we will focus on how multilevel models can be used for longitudinal data analysis. This class will cover the modelling of continuous, polynomial and discontinuous change models. We will consider equal and unequal times of measurement. Additionally, we will start to carefully look at the case and time specific residuals of the models. We will also discuss various covariance structures of random slopes.

The last class will extend the basic multilevel models covered in days 1 to 3 into the limited dependent variable situations. We will discuss how multilevel models can be generalized to dichotomous, categorical, ordinal, count and other types of dependent variables (much like in the case of linear regression, which students should be familiar with at the start of the course). We will also discuss the addition of a third (and possibly more) levels of analysis to the two-level models.

This description is subject to change at the discretion of the Instructor

2 Credits

For completion of all work before and during the course, as outlined by the Instructor, and 90% participation and attendance of the course.

2 Additional Credits

Course specific extra assignments. These can include submitting assignments before the course, daily assignments, and/or a final assignment to be completed after the course as decided by the Instructor.