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Workshops & seminars, Conferences & lectures

Introduction to Hierarchical Modelling (San Juan, Puerto Rico)

with Dr. Jeff Gill,
Distinguished Professor, Departments of Government and Mathematics & Statistics, Director, Center for Data Science, American University

SPSA - San Juan, Puerto Rico 2020
Thursday, January 9, 2020
2 p.m. – 6:20 p.m.

Dr. Jeff Gill,
Distinguished Professor, Departments of Government and Mathematics & Statistics, Director, Center for Data Science, American University


Participants must register to attend: Register here


WSSR Coordinator
514-848-2424 x5473


SPSA Conference 2020
San Juan, Puerto Rico


This workshop introduces hierarchical/multilevel regression-style linear models (and a few basic nonlinear forms) in a manner accessible to social and behavioral scientists. These models account for levels of aggregation that are typical in social science data in which individuals are nested in groups, and possibly multiple groups. Since these specifications are inherently Bayesian in nature this workshop will also introduce the basic principles of Bayesian statistics to students in the social and behavioral sciences without requiring an extensive background in mathematical statistics. Most of the examples will be drawn from sociology, political science, economics, marketing, psychology, public policy, and anthropology.

The prerequisites for this workshop are a linear regression course and knowledge of matrix algebra. The emphasis will be on applying the principles to actual data-analytic problems of interest to participants rather than through textbook examples. The workshop will make extensive use of software that is in the public domain, yet is high in quality (including R and JAGS), please make sure to bring a personal laptop with both programs installed.

Workshop Outline & Reading List

Thursday, January 9

Multilevel Models

  1. Advantages of Multilevel Models
  2. Features of Multilevel Models
  3. Modern Notation
  4. Linear Model Illustration
  5. Vocabulary Overview
  6. Comparison with Variable Contrasts
  7. Partial Pooling Estimates with No Explanatory Variables
  8. Contrasting Pooling Approaches
  9. Presenting Results from Multilevel Models
    1. Simple Illustration of Bayesian Inference
    2. Specifications with the lmer() Function
  10. A Bayesian Take on Hierarchical Models
  11. Panel Data as Group Membership
  12. Varying Intercept Logit Multilevel Model
  13. Bayesian Multinomial Specifications for Employment Status
  14. Random Effects Example for Indomethacin Trials
  15. Nested Classification Factors
  16. Simple Linear Bayesian Specification: Poverty Among the Elderly, Europe
  17. Prior Sensitivity, ANES Data from 2012
  18. Logit Model for Survey Responses in Scotland, Percent Predicted Correctly
  19. Another application: Poisson Model of Military Coups

King, Gary (1986) “How Not to Lie With Statistics: Avoiding Common Mistakes in Quantitative Political Science”. American Journal of Political Science, 30, 666-687, 1986.

Gill, Jeff and Andrew J. Womack (2013) “The Multilevel Model Framework”. In The SAGE Handbook of Multilevel Modeling. Scott, Marc A, Jeffrey S Simonoff and Brian D Marx (eds). London: SAGE Publications Ltd, pp. 3-20. SAGE Research Methods.

Gill, Jeff and Chris Witko (2013) “Bayesian Analytical Methods: A Methodological Prescription for Public Administration”. Journal of Public Administration Research and Theory, 23:2, pp. 457-494.

Snijders Tom A.B. (2011) “Multilevel Analysis”. In International Encyclopedia of Statistical Science. Lovric M. (eds). Berlin: Springer.

Gelman, Andrew (2006) “Multilevel (Hierarchical) Modeling: What It Can and Cannot Do”. Technometrics, 48:3, pp. 432-435.

Government 2003: Bayesian Hierarchical Models (Harvard University), some code and references at

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