Multilevel Statistical Methods: Concept and Application (SHH 263)

Course Description

This course is designed to provide you with a training experience in the concept and application of multilevel statistical modeling.  You will be motivated to think about correlated and dependent data structures that arise due to sampling design and/or are inherent in the population (such as pupils nested within schools; patients nested within clinics; individuals nested within neighborhoods and so on).  The substantive purpose of this course is to enable quantitative assessments on the role of contexts (e.g., schools, clinics, neighborhoods) in predicting individual outcomes.  This will be accomplished by developing a range of multilevel models along with a detailed discussion of the statistical properties and the interpretation of each model.  Empirical presentations and homework assignments will focus on multilevel analysis using MLwiN – a specialized software to handle models with complex data structures.

Course Materials

The required course text is a manual written by S V Subramanian and Kelvyn Jones, Multilevel Statistical Models.  Additional reading may be prescribed during the course.  Class handouts will be made available on the day of the class, and will be uploaded onto the course website after the class.

Course Objectives

By the end of the course, you will be able to:

  • Conceptualize a scientific problem that requires a multilevel approach, and identify the appropriate multilevel structure.
  • Manage data for statistical modeling of hierarchic structures.
  • Describe the basic principles of multilevel regression modeling using graphical, verbal and statistical language.
  • Apply and implement modern methods for the analysis of clustered data and heterogeneity.
  • Develop a variety of models that enable quantitative assessment of contextual effects.
  • Interpret and communicate the substantive meaning of results from simple and complex multilevel models.
  • Utilize MLwiN procedures to perform multilevel analyses. 

Course Organization and Format

The course will be lecture-based, with substantial hands-on component.  The general pattern in the lectures would be to introduce different methodological concepts, graphically and verbally followed by their statistical specification.  Emphasis will be placed on interpreting results obtained from a multilevel model.  Lectures will be complemented by class-room participation (including calling upon students to respond to questions from the assigned readings and case studies) and in-class demonstration of specifying, fitting and interpreting multilevel models using MLwiN.  The learning of the software will be integrated with the statistical concepts.

Course Home Page

Course Schedule

  • Introduction
  • Multilevel study design and structures
  • Varying relationships: a graphical introduction to multilevel models
  • Random intercepts model (using continuous predictor)
  • Random slopes model (using continuous predictor)
  • LAB: Fitting random intercepts and slopes models in MLwiN
  • Fixed versus random effects: a comparative perspective
  • Modeling variance function
  • Modeling heteroskedasticity
  • LAB: Significance testing and interpreting variance functions in MLwiN
  • Categorical predictors in multilevel models (Fixed part, Level-2)
  • LAB: Fitting random intercepts and slopes models in MLwiN with categorical predictors
  • Categorical predictors in multilevel models – Level-1
  • Higher level predictors in multilevel models
  • LAB: Higher level predictors in multilevel models
  • Linear multilevel regression models: review and discussion
  • Interpreting Three-level Model
  • Logistic multilevel models
  • LAB: Logistic multilevel models in MLwiN
  • Marginal versus Mixed models: Case Study
  • Applied Longitudinal Analysis
  • Multilevel models and public health practice
  • Causal ecologic effects