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Multilevel Structural Equation Modelling

Bruno Castanho Silva

University of Cologne

Bruno Castanho is a postdoctoral researcher at the Cologne Center for Comparative Politics, University of Cologne.

He holds a PhD in political science from Central European University and has experience teaching various topics in research design and methodology, including causal inference, machine learning, and structural equation modelling. 

Bruno has written a textbook on Multilevel Structural Equation Modelling in collaboration with fellow Winter School instructors Constantin Manuel Bosancianu and Levi Littvay.



Course Dates and Times

Monday 22 ꟷ Friday 26 March 2021
2 hours of live teaching per day
14:00 ꟷ 16:00

Prerequisite Knowledge

This course assumes a working knowledge of multilevel modelling (MLM) and structural equation modelling (SEM). You should know what are path and confirmatory factor models, and you should understand random intercept and slope models (also known as fixed and random effects).

You may use one of these techniques regularly, but not the other – in which case, this course is ideal for you.

Basic knowledge of Mplus is helpful but not required.

Short Outline

This course provides a highly interactive online teaching and learning environment, using state of the art online pedagogical tools. It is designed for a demanding audience (researchers, professional analysts, advanced students) and capped at a maximum of 16 participants so that the teaching team (the Instructor plus one highly qualified Teaching Assistant) can cater to the specific needs of each individual.

Purpose of the course

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

Multilevel modelling allows us to assess data on multiple levels of analysis provided 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, etc.

Structural equation models 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 (MLSEM) 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 Mplus.  

In this course we will go though the most common applications of multilevel structural equation models with examples in Mplus.

ECTS Credits

3 credits Engage fully with class activities 
4 credits Complete a post-class assignment

Long Course Outline

Key topics covered

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-friendlly 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. 


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, and have an intro to Mplus.


Multilevel path analysis.


We cover multilevel confirmatory factor analysis.


We discuss full stuctural models in a multilevel framework.


We discuss advanced topics. Students give presentations on their own projects / data.

How the course will work online

Reading materials, including the main course textbook, will be provided by the Instructor. Readings will be supplemented by around 60–90 minutes of prerecorded lectures each day covering the theoretical part of the materials. There will be around seven hours of live sessions during the week.

The live sessions are mainly devoted to:

  • Q&A with the Instructor
  • lab sessions during which the Instructor will demonstrate how to use Mplus and R for MSEM
  • student presentations during the seminar on the last day.

The live components will also include getting to know each other on the first day and, potentially, an online social event. You are welcome to set up appointments with the Instructor or TA for one-to-one consultations, during office hours.

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.