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Multilevel Structural Equation Modelling

Levente Littvay

Central European University

Levente Littvay researches survey and quantitative methodology, twin and family studies and the psychology of radicalism and populism.

He is an award-winning teacher of graduate courses in applied statistics with a topical emphasis in electoral politics, voting behaviour, political psychology and American politics.

He is one of the Academic Convenors of ECPR’s Methods School, and is Associate Editor of Twin Research and Human Genetics and head of the survey team at Team Populism.


Course Dates and Times

Monday 5 – Friday 9 August 09:00–10:30 and 11:00–12:30

Prerequisite Knowledge

This is an upper-intermediate to advanced level course. You should have working knowledge of multilevel modelling (MLM) and structural equation modelling (SEM).

You should understand what path models, confirmatory factor models and the combination of these two models are. You also need an understanding of random intercept and slope models.

Most people taking this course will regularly use either MLM or SEM, but not the other. If you are one of these people, I will do a quick review of both techniques on Day 1, but I still strongly urge you to first take, at least, the first week of the other class where your knowledge is lacking. 

Alternatively, you can prepare independently. To review structural equation modelling, I recommend Rex B. Kline's Principles and Practice of Structural Equation Modeling (any edition). For multilevel modelling, Douglas A. Luke's Multilevel Modeling. If you are struggling to follow these texts, register for either Introduction to Structural Equation Modelling or Applied Multilevel Regression Modelling, as appropriate.

I will assume you have basic knowledge of R or Mplus. If you don’t, sign up for R Basics.

Short Outline

Structural equation modelling (SEM) and multilevel modelling (MLM) are popular analytical methodologies in the social sciences today.

MLM allows us to assess data on multiple levels of analysis as long as the sample size, on both levels, is sufficient for large n analysis. Most common applications are international surveys that are starting to approach these sample size requirements. But applications also include within person designs, regional analyses, students nested within schools, patients nested within hospitals or employees nested within firms.

SEMs combine the power of factor analysis, flushing out measurement error and path analysis which are, in essence, simultaneous regression models considering complex causal structures between our observed variables or factors.

Multilevel structural equation modelling (MSEM) is marriage between the two methods in which structures of relationships can be assessed at multiple levels of analysis. While computationally complex, these methods are effectively implemented in a user-friendly way in both R and Mplus. In this course we will go though the most common applications of multilevel structural equation models, with examples.

ECTS Credits for this course

3 Credits Complete a take-home exam over the weekend after the course. 

4 Credits As above, plus write a paper using the method (strictly), due three weeks after the completion of the course.

Long Course Outline

An ever-increasing number of software packages are implementing multilevel approaches to SEMs. While computationally, analytically and structurally complex, these methods are effectively implemented in a user-friendly way in R and Mplus (also Stata).

In this course we will go though the most common applications of MSEMs with examples in R and Mplus. 

Mplus has several advantages (user friendly, flexible) but clear disadvantages (expensive, closed). Developers of the R package for SEM: Lavaan also started to implement MSEM applications. Significantly less flexible than Mplus, most models in the book we use for the course can be estimated with R using the Lavaan package. All examples used in the course will run in the free demo version of Mplus. 

Please bring your laptop with R + Lavaan and/or Mplus (Demo) installed. R and Mplus are compatible with Windows, Mac and Linux. Android and iOS are inadequate for the purposes of this course but they will run on Project Crostini compatible Chromebooks in the Linux sandbox.

Monday We spend some time getting to know each other and reviewing the most important components of MLM and SEM. We go into notation to define our MSEMs (may reach into Tuesday).

Tuesday We start with multilevel path analysis.

Wednesday We cover multilevel confirmatory factor analysis.

Thursday We discuss full structural models in a multilevel framework.

Friday We discuss advanced topics and the various conceptualisations for defining MSEMs.

The course, for the most part, is focused on theory and the understanding of the models at hand. We will review applications and arm you with the tools to run your own models, but the course will not be software focused for the most part. You are coming here to learn MSEM, not just how to run models in one software or another. (My teaching philosophy is, once you know what you are doing, software is easy. If you don’t know what you are doing and want to compensate by learning more software without proper foundations, you are doing it wrong anyway.)

Day Topic Details
1 Meet and greet, Review MLM and SEM, Notation.


2 Multilevel Path Models

Lecture + Lab (in lecture room on laptops)

3 Multilevel CFA

Lecture + Lab (in lecture room on laptops)

4 Multilevel Structural Equation Models

Lecture + Lab (in lecture room on laptops)

5 Advanced Topics

Lecture + Lab (in lecture room on laptops)

Day Readings

Rex B. Kline
Principles and Practice of Structural Equation Modeling
(any edition or equivalent)

Douglas A. Luke (2004)
Multilevel Modeling (Sage) or equivalent

Silva et al Chapter 1


Silva et al Chapter 2


Silva et al Chapter 3


Silva et al Chapter 4


Silva et al Chapter 5 (+ maybe Mehta & Neale 2005)

Software Requirements

Bring your laptop with R and Mplus free demo version installed. Both work on Windows, Mac and Linux.

Hardware Requirements

Bring your laptop with R and Mplus free demo version installed.


Mandatory before the start of the course

Kline, R. B. (2015). Principles and Practice of Structural Equation Modeling
New York: The Guilford Press. (Earlier editions are fine as well)

Luke, D. A. (2004). Multilevel Modeling
Thousand Oaks, CA: Sage Publications

Mandatory for the course

Silva, B.C., Bosancianu, C.M. & Littvay, L (2019). Multilevel Structural Equation Modeling

(if we get to it)
Mehta, P.D. & Neale, M.C. (2005) 'People Are Variables Too: Multilevel Structural Equations Modeling'
In Psychological Methods 10(3):259-284.

Additional readings

Heck, R. H., & Thomas, S. L. (2015). An Introduction to Multilevel Modeling Techniques: MLM and SEM Approaches Using Mplus
New York: Routledge

Hox, J. J. (2010). Multilevel Analysis: Techniques and Applications
Second edition. London: Routledge

Stapleton, L. M. (2006). 'Using Multilevel Structural Equation Modeling Techniques with Complex Sample Data'
In G. R. Hancock & R. O. Mueller (Eds.), Structural Equation Modeling: A Second Course (pp. 345–383). Charlotte, NC: Information Age Publishing

Byrne, B. M. (2011). Structural Equation Modeling with Mplus: Basic Concepts, Applications, and Programming
London: Routledge. (Especially the last chapter)

Additional Information


This course description may be subject to subsequent adaptations (e.g. taking into account new developments in the field, participant demands, group size, etc). Registered participants will be informed in due time.

Note from the Academic Convenors

By registering for this course, you confirm that you possess the knowledge required to follow it. The instructor will not teach these prerequisite items. If in doubt, contact the instructor before registering.