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Regular version of the site

Multilevel Models

Academic Year
Instruction in English
ECTS credits
Course type:
Elective course
1 year, 3, 4 module

Course Syllabus


Many data structures are nested: students nested within classrooms, workers nested within business units, observations nested within individuals, et cetera. Until recently, dealing with nested data structures has been difficult both conceptually and computationally. New models that have been termed multilevel models (also known as hierarchical [non]linear models, mixed effects models, or random coefficient models) lead to separating the lower level effects and the higher level effects explicitly into different parts (e.g., Level 1, Level 2, etc.) of the same overarching model. Such models are designed to avoid “aggregation bias” and to solve the “unit of analysis” problem, all while appropriately accounting for the correlated nature of the “within unit” observations. This course will introduce students to the general multilevel model with an emphasis on applications. We will discuss how such models are conceptualized, the meaning and interpretation of the parameter estimates, and finally how to implement them in computer programs. A major emphasis throughout the course will be on how to choose the appropriate model so that specific questions of interest can be addressed in a methodologically sound way.
Learning Objectives

Learning Objectives

  • The course gives students an important foundation to develop and conduct their own research as well as to evaluate research of others.
Expected Learning Outcomes

Expected Learning Outcomes

  • Know the theoretical foundation of multilevel modeling.
  • Know modern extensions to hierarchical modeling.
  • Know the basic principles behind working with all types of data for building multilevel models.
  • Be able to explore the advantages and disadvantages of various hierarchical modeling instruments, and demonstrate how they relate to other methods of analysis.
  • Be able to work with major linear modeling programs, especially R, so that they can use them and interpret their output.
  • Be able to develop and/or foster critical reviewing skills of published empirical research using applied statistical methods.
  • Be able to criticize constructively and determine existing issues with applied linear models in published work.
  • Have an understanding of the basic principles of hierarchical models and lay the foundation for future learning in the area.
  • Have the skill to meaningfully develop an appropriate model for the research question.
  • Have the skill to work with statistical software, required to analyze the data.
Course Contents

Course Contents

  • Introduction to the Framework of Hierarchical Modeling
    The first session will focus on understanding hierarchical / multilevel data structures and applica-tions multilevel models.
  • Random effects
    The session discusses analysis of variance and covariance with random effects and choosing the location of independent variables.
  • Parameter interpretation
    The session provides the theoretical basis for the meaning and interpretation of parameters, hy-pothesis testing, fixed and random effects, and model evaluation.
  • Nesting I
    This sessions builds the understanding of cross-sectional nested data structures.
  • Nesting II
    This session covers the foundation of longitudinal data structures and nesting in longitudinal context.
  • Multiple levels
    This session will introduce the multi-center data structures and three-level multilevel models. It will also cover the estimation theory for multilevel models.
  • Issues in multilevel modeling
    This session will focus on missing data issues and error structures for multilevel models; other statistical and methodological issues in MLM.
  • Extensions I
    This session will provide an overview of extension of multilevel models to a more general latent variable models.
  • Extensions II
    This session will cover design consideration for nested data structures.
Assessment Elements

Assessment Elements

  • non-blocking Final In-Class or Take-home exam (at the discretion of the instructor)
  • non-blocking Homework Assignments (5 x Varied points)
  • non-blocking In-Class Labs (9-10 x Varied points)
  • non-blocking Quizzes (Best 9 of 10, Varied points)
Interim Assessment

Interim Assessment

  • Interim assessment (4 module)
    0.5 * Final In-Class or Take-home exam (at the discretion of the instructor) + 0.2 * Homework Assignments (5 x Varied points) + 0.2 * In-Class Labs (9-10 x Varied points) + 0.1 * Quizzes (Best 9 of 10, Varied points)


Recommended Core Bibliography

  • Antony, J. S., & Lott, J. L. (2012). Multilevel Modeling Techniques and Applications in Institutional Research : New Directions in Institutional Research, Number 154. San Francisco: Jossey-Bass. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=464973
  • Little, T. D. (2013). Longitudinal Structural Equation Modeling. New York: The Guilford Press. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=544777
  • Meijer, E., & Leeuw, J. de. (2008). Handbook of Multilevel Analysis. New York: Springer. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=261439
  • Smith, R. B. (2011). Multilevel Modeling of Social Problems : A Causal Perspective. Dordrecht: Springer. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=371921
  • Wang, J., Xie, H., & Fisher, J. (2011). Multilevel Models : Applications Using SAS®. Berlin: De Gruyter. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=430112

Recommended Additional Bibliography

  • Agresti, A. (2015). Foundations of Linear and Generalized Linear Models. Hoboken, New Jersey: Wiley. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=941245
  • Lindsey, J. K. (1997). Applying Generalized Linear Models. New York: Springer. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=104525
  • Rutherford, A. (2001). Introducing Anova and Ancova : A GLM Approach. London: SAGE Publications Ltd. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=251737