Multilevel/Hierarchical Modeling

It was a pleasure to attend Prof. Karreth's course. He is highly enthusiastic and knowledgeable, and his lecture slides, lab notes, and practical guides were extremely helpful. — participant from Singapore

This course introduces participants to the analysis of multilevel, hierarchical, or structured data. These data are ubiquitous in all of the social sciences and include observations that are ‘nested’ in higher-level units, such as groups of survey respondents in different countries, students in different schools, or country-level observations at repeated time points. Analyzing multilevel data can be challenging, but provides many opportunities for statistical inference. Participants will learn how to appropriately estimate such quantities of interests as effects that vary across units and/or time or how much of a change in an outcome of interest is associated with individual- or group-specific features.


This course was offered in 2018.


Johannes Karreth (picture), Ursinus College

Detailed Description

This course provides participants with an applied introduction to basic and advanced approaches to the quantitative analysis of multilevel data, which is commonly known as multilevel, hierarchical, or mixed regression modeling. Multilevel data are ubiquitous in social science and include observations that are ‘nested’ in higher-level units, such as groups of survey respondents in different countries, students in different schools, or country-level observations at repeated time points.

Participants will learn how to estimate appropriate models for multilevel data across a wide variety of contexts, including differences between groups, across time, and effects that vary between groups or across time. The course also addresses choice modeling in multilevel data structures, e.g., to estimate public opinion in small areas from large national surveys, using multilevel regression with post-stratification (MRP), as well as how to use multilevel modeling for time-series cross-sectional data.

Covering both theory and practical applications, the course will explore the following topics:

  • Characteristics of multilevel data structures

  • Data management for multilevel data

  • Fixed and random effects

  • Multilevel regression for continuous and categorical outcomes

  • Multilevel regression for time-series cross-sectional data

  • Multilevel regression and post-stratification

  • Post-estimation (incl. marginal effects and predicted probabilities)

  • Model assessment and comparison

Upon completion of this course, participants will be able to:

  • Understand how multilevel/hierarchical/structured data challenge the assumptions of pooled, i.e., standard, regression models

  • Distinguish the concepts of fixed and random effects in the context of multilevel data

  • Estimate regression models with varying slopes and varying intercepts

  • Generate such post-estimation quantities as marginal effects, predicted probabilities, etc. from multilevel regression models

  • Use graphical tools to present results from multilevel regression models

The course content will be reinforced through regular hands-on exercises. Participants will learn how to use the free and open-source software packages R to manage multilevel data, analyze their own multilevel data, and to communicate their results to a broader audience.


Participants should be familiar with basic statistics and the core concepts of linear regression. However, even participants with limited prior experience will be able to effectively participate as the course begins with a quick review of regression as it relates to multilevel data.


Participants are expected to bring a WiFi-enabled laptop computer. Access to data, temporary licenses for the course software, and installation support will be provided by the Methods School.

Core Readings

Gelman, Andrew, and Jennifer Hill. 2007. Data Analysis Using Regression and Multilevel/Hierarchical Models. New York, NY: Cambridge University Press.

Suggested Readings

Snijders, Tom A. B., and Roel J. Bosker. 2012. Multilevel Analysis: An Introduction to Basic and Advanced Multilevel Modeling. 2nd edition. Thousand Oaks, CA: Sage Publications.

Raudenbush, Stephen W., and Anthony S. Bryk. 2002. . Hierarchical Linear Models: Applications and Data Analysis Methods. Thousand Oaks, CA: Sage Publications.

Monogan, James E. 2015. Political Analysis Using R. Cham: Springer.

Teetor, Paul. 2011. R Cookbook. Sebastopol, CA: O'Reilly Media.