Multilevel and Mixed Models Using R

A 2-Day Seminar Taught by Stephen Vaisey, Ph.D.

Read reviews of other seminars taught by Stephen Vaisey

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.

This two-day 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. (For more on panel data, see Longitudinal Data Analysis Using R, which will be taught immediately after this course.)

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, students 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.


To participate in the hands-on exercises, you are strongly encouraged to bring a laptop computer. The vast majority of what you will learn in this course can be applied in any software package. This seminar will mostly use R for empirical examples and exercises. To replicate the instructor’s workflow in the course, come with R and RStudio installed on your computer. However, no previous experience with R is needed because all code will be provided. Although the course will be taught in R, complete Stata syntax for all analyses will be provided on request.

Who should attend? 

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

LOCAtion, Format, And Materials 

The class will meet from 9 am to 5 pm each day with a 1-hour lunch break at Temple University Center City, 1515 Market Street, Philadelphia, PA 19103. 

Participants receive a bound manual containing detailed lecture notes (with equations and graphics), examples of computer printout, and many other useful features. This book frees participants from the distracting task of note taking. 

Registration and lodging

The fee of $995.00 includes all seminar materials.

Refund Policy

If you cancel your registration at least two weeks before the course is scheduled to begin, you are entitled to a full refund (minus a processing fee of $50). 

Lodging Reservation Instructions 

A block of guest rooms has been reserved at the Club Quarters Hotel, 1628 Chestnut Street, Philadelphia, PA at a special rate of $137 per night. This location is about a 5 minute walk to the seminar location. In order to make reservations, call 203-905-2100 during business hours and identify yourself by using group code STA729 or click here. For guaranteed rate and availability, you must reserve your room no later than Friday, June 29, 2018. 

If you make reservations after the cut-off date, ask for the Statistical Horizons room rate (do not use the code) and they will try to accommodate your request.


  • 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


“Dr. Vaisey is a great teacher who is able to impart a significant amount of insight and understanding in a short period of time. Great energy and enthusiasm, very clear. Thanks so much. What I’ve learned is very valuable.”
  Kenneth Coburn, Healthy Quality Partners

“The instructor had excellent mastery of the topic and yet was able to translate his knowledge with great clarity to those new to the concepts. I appreciated his consistent employment of real-world examples to help solidify my understanding of a technique’s applications.”
  Emily Hawks, Adobe Systems

“Stephen Vaisey is a remarkable instructor. His command of the subject is outstanding and his ability to communicate the course content is impressive. He uses numerous examples and takes various approaches to explain concepts through the seminar. Such intense introductions have a tendency to feel long and tiring, so I was pleasantly surprised to find that this seminar was often fun and surprisingly engaging!”
  Andrew Dierkes, University of Pennsylvania

“Steve is the professor I wish I’d had in graduate school. He is a black belt at theory and technical details, and has the ability to communicate the materials in a way that helps you to grow an intuition. This is a rare quality in a statistician and teacher, and Steve nails it. He exhibits humor, thoughtful questions and responses, and the ability to anticipate where people get “stuck.” Take a course from Steve and you’ll be glad you did it!”
  Andy Bogart, RAND Corporation

“Stephen did an excellent job making difficult concepts easy to understand through examples and clear explanations. I learned how to better interpret, compare, and create practical models, all of which apply to many research projects with which I am involved.”
  Scott Friedlander, Los Angeles Biomedical Research Institute