Multilevel and Mixed Models Using R

A 3-Day Remote Seminar Taught by
Stephen Vaisey, Ph.D.

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To see a sample of the course materials, click here.

Multilevel models are a class of regression models for data that have a hierarchical (or nested) structure. Common examples of such data structures are students nested within schools or classrooms, patients nested within hospitals, or survey respondents nested within countries. Using regression techniques that ignore this hierarchical structure (such as ordinary least squares) can lead to incorrect results because such methods assume that all observations are independent. Perhaps more important, using inappropriate techniques (like pooling or aggregating) prevents researchers from asking substantively interesting questions about how processes work at different levels.

Starting February 11, we are offering this seminar as a 3-day synchronous*, remote workshop. Each day will consist of a 4-hour live lecture held via the free video-conferencing software Zoom. You are encouraged to join the lecture live, but will have the opportunity to view the recorded session later in the day if you are unable to attend at the scheduled time.

Each lecture session will conclude with a hands-on exercise reviewing the content covered, to be completed on your own. An additional session will be held Thursday and Friday afternoons as an “office hour”, where you can review the exercise results with the instructor and ask any questions.

*We understand that scheduling is difficult during this unpredictable time. If you prefer, you may take all or part of the course asynchronously. The video recordings will be made available within 24 hours of each session and will be accessible for two weeks after the seminar, meaning that you will get all of the class content and discussions even if you cannot participate synchronously.


This seminar provides an intensive introduction to multilevel models. After a brief conceptual introduction (including a discussion of the difference between random and fixed effects), we will begin with simple variance components models that can tell us how much of the variation in a measure can be attributed to different levels of observation. We will then move on to mixed models (random effects models with fixed covariates) that allow us to ask how factors at different levels can affect an outcome.

Next, we will investigate how using random coefficients and cross-level interactions can help us discover hidden structure in our data and help us investigate how individual-level processes work differently in different contexts. We will also briefly consider how these techniques can be applied to cases where we have repeated observations of individuals or other entities over time.

Although the course will focus primarily on the continuous outcome case, we will also briefly cover how these models can easily be extended for use with categorical and limited dependent variables.

The seminar will focus on hands-on understanding and draw from examples across the social and behavioral sciences. At the conclusion of the course, you will:

  1. Know the technical and substantive difference between fixed and random effects.
  2. Understand random intercepts, random coefficients, and crossed random effects models and know when to use each one.
  3. Know how to combine the strengths of random-effects and fixed effects approaches into a single model.
  4. Know how to estimate these models and interpret the results.


This remote seminar is held via Zoom, a free video conferencing application. Instructions for joining a session via Zoom are available here. Before the seminar begins, you will receive an email with the meeting code and password you must use to join.  

The vast majority of what you will learn in this course can be applied in any software package. However, this seminar will mostly use R for empirical examples and exercises. To replicate the instructor’s workflow in the course, you should have R and RStudio already installed on your computer when the course begins. No previous experience with R is needed, however, because all necessary code will be provided. For those who prefer Stata, complete Stata code for all analyses will be provided on request.

If you’d like to take this course but are concerned that you don’t know enough R, there are excellent on-line resources for learning the basics. Here are our recommendations.

WHO SHOULD Register? 

This course is for anyone who want to learn to apply multilevel models to observational data. You should have a basic foundation in linear regression.


  • What are multilevel models?
  • Hierarchical linear model motivation and notation
  • Within and between variance
  • Variance components models and plots
  • The first distinction between “random” and “fixed” effects
  • “Shrinkage” and empirical Bayes estimates of intercepts
  • What are mixed models a mix of?
  • Three types of R-squared
  • Random coefficients/slopes
  • Model selection with BIC and AIC
  • Basic diagnostics
  • The second distinction between “random” and “fixed” effects
  • When and why (not) to use random effects models
  • Testing the random effects assumption
  • The “between-within” method to combine the best of RE/FE
  • Centering and cross-level interactions
  • A brief comparison of clustered and panel data
  • Multilevel logistic regression and other limited dependent variables
  • Presenting results

REVIEWS OF Multilevel and Mixed Models Using R

“Excellent course! The combination of Dr Vaisey’s instructions and humor is very important in the process of learning. I would highly recommend this course for anyone who needs to gain an understanding of MLM!”
  Anastasia Vatou, Aristotle University of Thessaloniki

“Dr. Vaisey was an amazing instructor.  He explained complex models clearly and practically and in a way in which I could also apply the information to my own research. I came out of this course feeling much more confident in multilevel and mixed model analysis.”
  Tara Powell, University of Illinois

“The Multilevel and Mixed Models Using R course provides the principles of multilevel modeling with easy to grasp examples. I would highly recommend the course.”
  Nathan O’Hara, University of Maryland