Multilevel Models

Multilevel Analysis and Group-Randomized Trials

Author

Francisco Cardozo, PhD

Published

March 20, 2026

Overview

In this class, we will cover the theory and practice of multilevel modeling for clustered and longitudinal data. We will learn why ignoring the dependence structure in grouped data leads to incorrect inferences, how mixed-effects models and GEE address this, and how to fit and interpret these models in R.

Learning Objectives

By the end of this lesson, you will be able to:

  1. Explain why independence of observations matters and what happens when it is violated
  2. Compute and interpret the Intraclass Correlation Coefficient (ICC) and the Design Effect
  3. Fit random-intercept and random-slope models using lme4 in R
  4. Distinguish between categorical and continuous time specifications in longitudinal models
  5. Compare and contrast mixed-effects models and GEE for clustered data

Topics

  • Intraclass Correlation
  • Design Effect
  • Cluster-randomized and non-randomized designs
  • Sandwich estimation

Materials

TipSlides

Access the class presentation slides:

View Class Slides

WarningAssignment

Assignment #7: TBD

Readings

Required

  • Enders, C. K., & Tofighi, D. (2007). Centering predictor variables in cross-sectional multilevel models: A new look at an old issue. Psychological Methods, 12(2), 121– 138. https://doi.org/10.1037/1082-989X.12.2.121
  • Raudenbush, S. W., Martinez, A., & Spybrook, J. (2007). Strategies for improving precision in group-randomized experiments. Educational Evaluation and Policy Analysis, 29(1), 5-29.

Supplemental

  • Geiser, C. (2013). Data Analysis with Mplus. Methodology in the Social Sciences, The Gildor Press. New York: NY [Chapter 5]
  • Murray, D. M., Varnell, S. P., & Blitstein, J. L. (2004). Design and analysis of group-randomized trials: a review of recent methodological developments. American Journal of Public Health, 94(3), 423-432.