ECPR Winter School
University of Bamberg, Bamberg
2 - 9 March 2018




WD213 - Multilevel Regression Modelling

Instructor Details

Instructor Photo

Levente Littvay

Institution:
Central European University

Instructor Bio

Levente (Levi) Littvay researches survey and quantitative methodology, twin and family studies (as the co-director of the Hungarian Twin Registry), and the psychology of radicalism and populism.

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

Levi is an Academic Convenor of ECPR’s Methods School and an Associate Editor of the journal Twin Research and Human Genetics.

 @littvay


Course Dates and Times

Monday 5 to Friday 9 March 2018
09:00-12:30
15 hours over 5 days

Prerequisite Knowledge

Solid understanding of multivariate linear and logistic regression analysis is required for the class, including an understanding of the assumptions of regression model, limited dependent variable models, understanding of link functions and the use of interactions. Please note that 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 the instructor considers as a “solid” understanding. I recommend a regression class to increase the depth of your knowledge on regression analysis before you take multilevel models. As an example, 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 both linear and logistic regression models you are prepared to take this course. If you do not have this foundation, I recommend an extra preparation before the course or (even better) an advanced regression class instead of multilevel modeling. This class is predominantly focused on teaching you multilevel modeling. We 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 make sure you bring your laptop to class with an up to date version of R (and whatever else you wish to use) installed.

Short Outline

The course is designed to provide scholars with a basic understanding of multilevel (a.k.a. hierarchical or mixed) models. Upon completion the students will have a basic conceptual understanding of multilevel modeling and its statistical foundations. Students will be able to critically assess the appropriateness of such techniques in their own and other people’s research. Special attention is given 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. While the course is predominantly designed to give you the knowledge of multilevel regression modeling, it does also arm you with the basic tools to run multilevel models in your choice of software such as R, Stata or SPSS. Please bring your laptops 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. The goal of the course is to offer a basic introduction and the foundation for students to start using and critically assessing multilevel models and also have the ability to independently discover and master advanced multilevel statistical topics.

Tasks for ECTS Credits

  • Participants attending the course: 2 credits (pass/fail grade) The workload for the calculation of ECTS credits is based on the assumption that students attend classes and carry out the necessary reading and/or other work prior to, and after, classes.
  • Participants attending the course and completing one task (see below): 3 credits (to be graded)
  • Participants attending the course, and completing two tasks (see below): 4 credits (to be graded)
  1. 2 ECTS Credits - Pass / Fail, attendance in 80% of the courses. Come prepared.
  2. 3 ECTS Credits - Graded, take home exam distributed on Friday, due Monday (after class) at noon.
  3. 4 ECTS Credits - same as above and a research paper due 2 weeks after the class using your own data and multilevel modeling
Long Course Outline

The course is designed to provide scholars with a basic understanding of multilevel models, which are also known as hierarchical models or mixed models. Upon completion, the students will have a basic conceptual understanding of multilevel models and their statistical foundations. Students will be able to critically assess the appropriateness of such techniques in their own and other people’s research. Special attention is given 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 conceptual, theoretical and statistical foundations will be presented and discussed. The minority of time we will be using a computer assessing 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 of the course is to offer a basic introduction to multilevel modeling so students 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. (Please carefully consult section 4 on requested prior knowledge.) The course will not cover the estimation theory behind multilevel models, so advanced mathematical knowledge or any knowledge of estimation theory is not required. Different estimations will, on the other hand, be discussed as necessary.

The first class will 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 modeling is and is not more appropriate. Along with an extensive discussion of the notion of nesting, common statistical notations and mathematical foundations will be covered in the first course.

The second course will focus on the more difficult aspects of multilevel models and starts discussing some of the assumptions the model makes. For example, understanding variance at multiple levels, interactions crosscutting levels of analysis, why centering is useful and possibly necessary will be discussed in the second class. In addition, we will extensively cover issues related to sample size and possible solutions for assumption violations in this realm.

The third class will 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 generalized to dichotomous, categorical, ordinal, count and other types of dependent variables (much like in the case of linear regression, which students should be familiar with at the start of the course). The third day, we will also discuss the addition of a third (and possibly more) levels of analysis to the two-level models.

On the fourth day we will focus on how multilevel models can be used for longitudinal analysis of change. This class will cover the modeling of continuous, polynomial and discontinuous change models. We will consider equal and unequal times of measurement and (if time allows) the equivalence of structural equation growth models with the multilevel change models. Additionally, we will start to carefully look 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.

On the final day I will 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 analyze data with such a structure. In addition to cross-classified models, the last class will be used to discuss other lingering issues and questions that might have emerged throughout the course.

Day-to-Day Schedule

Day 
Topic 
Details 
1Introduction to MLM 
2Cross-Level Interactions, Centering, Sample Size and Other Considerations 
3Limited Dependent Variables. Additional Levels of Analysis 
4Longitudinal Analysis 
5Cross-Classification 
Day-to-Day Reading List

Day 
Readings 
 Marco Steenbergen and Bradford Jones (2002) “Modeling Multilevel Data Structures.” American Journal of Political Science 46(1): 218-237.
 Douglas Luke (2004) Multilevel Modeling. Sage Quantitative Applications in the Social Sciences :London.
 Craig K. Enders and Davood Tofighi (2007) “Centering predictor variables in cross-sectional multilevel models: A new look at an old issue.” Psychological Methods 12(2): 121-138.
 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.
 Judith Singer and John Willett (2003) Applied Longitudinal Data Analysis: Modeling Change and Event Occurrence.Chapter 7: Examining the Multilevel Model’s Error Covariance Structure. New York: Oxford University Press.
 Fielding, Anthony, and Harvey Goldstein. 2006. “Cross-classified and Multiple Membership Structures in Multilevel Models: An Introduction and Review.” Research Report No. RR791, Department for Education and Skills, United Kingdom. Available at: http://dera.ioe.ac.uk/6469/1/RR791.pdf
 (OPTIONAL) Stephen W. Raudenbush and Anthony S. Bryk. (2001) Hierarchical Linear Models: Applications and Data Analysis Methods (2nd ed). Chapter 12: Models for Cross-Classified Random Effects. Newbury Park, CA: Sage.
Software Requirements

R (but will also provide Stata and SPSS examples)

Hardware Requirements

Students to bring their own laptops. Power outlets.

Literature


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:

HLM

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]

MlWin

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. http://www.bristol.ac.uk/cmm/software/mlwin/download/manual-print.pdf

Mplus

Linda Muthen and Bengt Muthen (2010) Mplus. Statistic Analysis with Latent Variables. User’s Guide. Muthen and Muthen. http://www.statmodel.com/download/usersguide/Mplus%20Users%20Guide%20v6.pdf

R

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. Springer.

Stata

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

SPSS

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

Disclaimer

The information contained in this course description form may be subject to subsequent adaptations (e.g. taking into account new developments in the field, specific participant demands, group size etc.). Registered participants will be informed in due time in case of adaptations.

Note from the Academic Convenors

By registering to this course, you certify that you possess the prerequisite knowledge that is requested to be able to follow this course. The instructor will not teach these prerequisite items. If you are not sure if you possess this knowledge to a sufficient level, we suggest you contact the instructor before you proceed with your registration.


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