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Political Research Exchange - PRX

WD213 - Multilevel Regression Modelling

Instructor Details

Instructor Photo

Levente Littvay

Central European University

Instructor Bio

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 25 February – Friday 1 March, 14:00 – 17:30 (finishing slightly earlier on Friday)
15 hours over five days

Prerequisite Knowledge

Solid understanding of multivariate linear and logistic regression analysis is required, including:

  • understanding of the assumptions of regression model
  • limited dependent variable models
  • understanding of link functions
  • use of interactions.

Knowing how to run a regression in software (knowing where to click and what to look for in the results output) does not constitute what I consider a 'solid' understanding.

If you know what heteroskedasticity is and how to diagnose it, why the independence of observation(’s residual)s are necessary in a regression model and if you know how to interpret and plot two-way interactions for linear and logistic regression models, you are prepared to take this course.

If you do not, I recommend extra preparation before the course or (even better) an advanced regression class.

This class is predominantly focused on multilevel modelling. I will also provide the basic tools for you to apply this knowledge with various software including R, Stata and SPSS. Some knowledge of at least one of these is necessary for you to get the most out of the class. I personally prefer R (and do not have SPSS or Stata licenses myself) and if you are in a similar situation, I recommend you use R for this class.

IMPORTANT – Please bring a laptop with an up-to-date version of R (and whatever else you wish to use) installed.

Short Outline

This course will teach you a basic conceptual understanding of multilevel (a.k.a. hierarchical or mixed) modelling and its statistical foundations.

You will learn how to critically assess the appropriateness of such techniques in your own and other people’s research.

I will pay special attention to the translation of theoretical expectations into statistical models, the interpretation of results in multilevel analyses and the general use and misuse of multilevel models in the social sciences.

The course also arms you with the basic tools to run multilevel models in software such as R, Stata or SPSS. Please bring your laptop with R (and, if it is not R, your preferred software) installed.

Applications will include models with continuous and limited dependent variables in hierarchical, longitudinal and cross-classified nesting situations.

By the end of the course, you will be able to use and critically assess multilevel models and to independently discover and master advanced multilevel statistical topics.

Tasks for ECTS Credits

2 credits (pass/fail grade) Attend at least 90% of course hours, participate fully in in-class activities, and carry out the necessary reading and/or other work prior to, and after, class.

3 credits (to be graded) As above, plus complete a take-home exam distributed on Friday, due Monday (after class) at noon.

4 credits (to be graded) As above, plus submit a research paper using your own data and multilevel modelling, due two weeks after the class.

Long Course Outline

The course will give you a basic understanding of multilevel models, also known as hierarchical models or mixed models. By the end of it, you will have a basic conceptual understanding of multilevel models and their statistical foundations. You will be able to critically assess the appropriateness of such techniques in your own and other people’s research.

I will pay special attention to the translation of theoretical expectations into statistical models, the interpretation of results in multilevel analyses, and to the general use and misuse of multilevel models in the social sciences. The class will shine a light on the contrast between what multilevel models are designed for and how they are most commonly used in the social sciences.

Most of the time we will spend with the blackboard (whiteboard), where I will present and discuss conceptual, theoretical and statistical foundations, although we will also spend some time using a computer to assess what multilevel models looks like mostly in R, but also in Stata and SPSS.

Please bring your own laptop to class with R installed, along with your favorite statistics software (in case it is not [yet] R).

We will cover models with continuous and limited dependent variables in hierarchical, longitudinal and cross-classified nesting situations. While the primary goal is to offer a basic introduction to multilevel modelling so you can start using and critically assessing work using such models, I also hope to provide the most studious scholars with enough foundation to independently discover and master other software packages and advanced multilevel statistical topics.

Multilevel modeling has close relations to both regression and analysis of variance models. The course will build on a regression foundation since regression models are more popular in the social sciences (with the possible exception of psychology). This is also the reason why a solid foundation in regression is necessary for all participants.

I will not cover the estimation theory behind multilevel models, so advanced mathematical knowledge or knowledge of estimation theory is not required. Different estimations will, on the other hand, be discussed as necessary.

Day 1

I introduce multilevel analysis and its relationship to regression models. We will discuss the analogous use of regressions (fixed effects) models, interaction models and the conditions under which multilevel modelling is and is not more appropriate. Along with an extensive discussion of the notion of nesting, I will cover common statistical notations and mathematical foundations.

Day 2

I focus on the more difficult aspects of multilevel models and discuss some assumptions the model makes. For example, understanding variance at multiple levels, interactions crosscutting levels of analysis, why centering is useful and possibly necessary. We will cover issues related to sample size and possible solutions for assumption violations in this realm.

Day 3

I extend the basic multilevel models covered in days 1 and 2 into the limited dependent variable situations. We will discuss how multilevel models can be generalised to dichotomous, categorical, ordinal, count and other types of dependent variables (much like in the case of linear regression, with which you should already be familiar). We discuss the addition of a third (and possibly more) levels of analysis to the two-level models.

Day 4

We focus on how multilevel models can be used for longitudinal analysis of change. We cover the modelling of continuous, polynomial and discontinuous change models. We consider equal and unequal times of measurement and (if time allows) the equivalence of structural equation growth models with the multilevel change models. We also start to look carefully at the case- and time-specific residuals of the models. Restrictions placed on these errors (on the error covariance matrix) can decrease the number of estimated parameters in a model, gaining valuable degrees of freedoms.

Day 5

I introduce cross-classified hierarchical models. Sometimes nesting happens in a structure where two sets of nesting groups are not mutually exclusive. One such example is when kids from different neighborhoods go to different schools and another is when kids attend different middle and high schools. In these situations, traditional hierarchical models are not useful but the closely related cross-classified models can accurately analyse data with such a structure. Finally, we discuss other lingering issues and questions that might have emerged throughout the course.


Day-to-Day Schedule

Day-to-Day Reading List

Software Requirements

R (but will also provide Stata and SPSS examples)

Hardware Requirements

Students to bring their own laptops. Power outlets.


Best introductory overview from the perspective of this class (simple, user friendly and uses SPSS):

Robert Bickel (2007)
Multilevel Analysis for Applied Research: It's Just Regression! (Methodology in the Social Sciences)
The Guilford Press

Important Articles

On Centering

Ita G.G. Kreft, Jan de Leeuw & Leona S. Aiken (1995) “The Effect of Different Forms of Centering in Hierarchical Linear Models.” Multivariate Behavioral Research 30(1): 1-21.

Enders, C.K. & Tofigh, D. (2007) “Centering predictor variables in cross-sectional multilevel models: A new look at an old issue.” Psychological Methods 12(2): 121-138.

Paccagnella, O. (2006). Centering or not centering in multilevel models? The role of the group mean and the assessment of group effects. Evaluation Review, 30(1), 66–85.

On Sample Size

Stegmüller, Daniel. (2013). How Many Countries for Multilevel Modeling? A Comparison of Frequentist and Bayesian Approaches. American Journal of Political Science, 57(3), 748–761.

Rahim Moineddin, Flora I Matheson and Richard H Glazier (2007) “A simulation study of sample size for multilevel logistic regression models.” BMC Medical Research Methodology 7:34

Classic Books

Stephen W. Raudenbush and Anthony S. Bryk. (2002) Hierarchical Linear Models: Applications and Data Analysis Methods (second ed.). Sage

Joop Hox (2002, 2010) Multilevel Analysis: Techniques and Applications. Routledge

Tom A. B. Snijders and Roel Bosker (1999, 2011) Multilevel Analysis: An Introduction to Basic and Advanced Multilevel Modeling. Sage

For Longitudinal Multilevel Analysis

Judith Singer and John Willett (2003) Applied Longitudinal Data Analysis: Modeling Change and Event Occurrence. Oxford University Press.

Software Applications


Raudenbush, S.W., Bryk, A.S., Cheong, Y.F., & Congdon, R.T. (2004)
HLM 7: Hierarchical linear and nonlinear modeling. Scientific Software International
[Included with Demo and Full Version of the Software]


Rasbash, J., Steele, F., Browne, W.J. and Goldstein, H. (2009)
A User’s Guide to MLwiN, v2.10. Centre for Multilevel Modelling
University of Bristol


Linda Muthen and Bengt Muthen (2010)
Mplus. Statistic Analysis with Latent Variables. User’s Guide
Muthen and Muthen


Andrew Gelman and Jennifer Hill (2007
Data Analysis Using Regression and Multilevel/Hierarchical Models
Cambridge University Press.

Paul Bliese (2012)
Multilevel Modeling in R
[though note that this is written by the author of the multilevel package in R and might have compatibility issues with other R packages like nlme or lme4]

Jose Pinheiro and Douglas Bates (2000, 2009)
Mixed Effects Models in S and S-Plus


Sophia Rabe-Hesketh and Anders Skrondal (2012)
Multilevel and Longitudinal Modeling Using Stata, Volume I: Continuous Responses, Third Edition
Stata Press

Sophia Rabe-Hesketh and Anders Skrondal (2012)
Multilevel and Longitudinal Modeling Using Stata, Volume II: Categorical Responses, Counts, and Survival, Third Edition
Stata Press


Heck, R.H., Thomas, S.L, and Tabata, L.N. (2010)
Multilevel and longitudinal modelling with IBM SPSS
New York: Routledge

Heck, R.H., Thomas, S.L, and Tabata, L.N. (2012)
Multilevel Modeling of Categorical Outcomes Using IBM SPSS
New York: Routledge

The following other ECPR Methods School courses could be useful in combination with this one in a ‘training track .
Recommended Courses Before

Summer School

Multiple Regression Analysis

Generalised Linear Models

Recommended Courses After

Summer School

Applied Multilevel Modelling II: Advanced Multilevel Modeling

Age-Period-Cohort Analysis

Advanced Topics in Applied Regression

Panel Data Analysis

Winter School

Multilevel Structural Equation Modelling

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.

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