Multilevel Models
Adv Multivariate Data Analysis
II -- SS08-CEP-935-001
Instructor  Y. M. Thum
Office Phone  517-423-9629
Office Address  450 Erickson Hall
Office Hours  MW 12:00 - 1:00 pm
Location  132 Erickson Hall
Times  MW 10:20 - 11:40 am

Required Text

Raudenbush, S. W. & Bryk, A. S. (2002, 2nd Edition). Hierarchical linear models in social and behavioral research: Applications and data-analysis methods. Newbury Park, CA: Sage.

Additional Resources

  1. Duncan C, Jones K, & Moon G. (1998). Context, Composition and Heterogeneity: Using Multilevel Models in Health Research. Social Science & Medicine. 46, 97-117.
  2. Seltzer, M. H. (1994) Studying variation in program success: A multilevel modeling approach. Evaluation Review, 18 (3), 342-361.
  3. Sullivan, L. M., Dukes, K. A. & Losina, E. (1999). Tutorial in Biostatistics: An Introduction to Hierarchical Linear Modeling. Statistics in Medicine, 18, 855-888.
  4. Willms, J.D. (1999). Basic concepts in hierarchical linear modeling with applications for policy analysis. In G. J. Cizek (Ed.), Handbook of Educational Policy (pp. 473-493).
  5. Bryk, A. S. & Raudenbush, S. W. (1987) Application of hierarchical linear models to assessing change. Psychological Bulletin, 101 (1), 147-158.
  6. Thum, Y. M. (1997) Hierarchical Linear Models for Multivariate Outcomes. Journal of Behavioral and Educational Statistics, 22 (1), 77-108.
  7. Singer, J. D. (1998). Using SAS PROC MIXED to fit multilevel models, hierarchical models, and individual growth models. Journal of Educational and Behavioral Statistics, 23, 323-355.
  8. Raudenbush, S.W. (2001). Toward a coherent framework for comparing trajectories of individual change. In, Collins, L. and Sayer, A. (Eds.), New methods for the analysis of change. Washington D.C.: The American Psychological Association (pp 35-64).

    HLM 6 Student Version may be downloaded for class use from Scientific Software. Also useful to the student is an on-line set of notes on the model and the program.

Course Description

Many research problems in the social sciences focus on the growth in knowledge and skills of individuals and of groups. In educational research, for example, children's growth in various natural settings such as the classroom and the school is typically the object of inquiry. However, understanding growth in organizational settings is fraught with difficulties under standard uni-level regression analyses. In fact, how to measure change and describe contextual effects on change, that is how to model nested processes, are two of the most troublesome and persistent methodological problems in the social sciences. This course is devoted to understanding these difficulties and their possible resolution using a multilevel, or hierarchical, modeling framework. The course will consider the statistical foundations of multilevel linear models, also known as hierarchical linear models (HLMs), and focuses on their application in behavioral and educational research.

Course Objectives

Students will examine in detail a variety of multilevel or hierarchical models appropriate for a broad range of applications.  The class will begin with an introduction to the hierarchical linear model (HLM), relating the HLM to the general linear model (e.g. Regression & ANOVA).  The focus on the linear model will be followed with coverage of non-linear models, growth models, and alternative designs (e.g., cross-nesting—student within neighborhoods and schools).  Topics discussed within the context of each multilevel model include hypothesis testing, evaluation of model fit, and computer packages that can be used to estimate the various multilevel models. Students will be exposed to selected advanced topics to be determined by the instructor.

Tentative Schedule

Date Topic Readings


Overview of Class
Introduction to Multilevel/Hierarchical Linear Models (HLMs)

 RB  Chap 1


Review of Regression & Analysis of Variance
Rudimentary Matrix Algebra
Centering Predictors, & Dummy variables

 Class Notes


The Logic of HLMs

 RB Chap 2


Martin Luther King Holiday



The General Hierarchical Linear Model
Examples & Interpretations

RB Chap 2 


An Introduction to HLM-6

Class Notes 


Applications in organizational research
Centering Predictors, revisited

RB Chap 5   


Theory: Estimation, Inference, & Hypothesis Testing

RB Chap 3   


Illustrations: Estimation, Inference, & Hypothesis Testing

RB Chap 4
Assign #1


Building HLMs

RB Chap 9 
2/13 Tools for Model assumptions, fit, and comparison RB Chap 9 
2/18 Growth Models as HLMs RB Chap 6 
2/20 More on Multilevel Growth Models

RB Chap 6  


Multilevel models & Mixed-Effects Models

Class Notes
 Assign #2

Interpreting software output

Class Notes



3/10 Random-Effects Meta-analysis
Other L1 variances known cases
RB Chap 7
Assign #3

Three-Level Models (HLM-3s)

RB Chap 8 

Applications of HLM-3s

RB Chap 8
Assign #4
3/19 A Brief Introduction to Factor Analysis
Latent Variable Regression (LVR) in HLMs
RB Chap 11
3/24 LVR Examples RB Chap 11 
3/28 AERA -- March 24-28  
3/31 To be announced.  
4/02 Models for Cross and Nested Designs (HCM-2s) RB Chap 12 

Examples of HCM-2s

RB Chap 12
4/09 Introduction to non-linear regression Class Notes
4/14 Hierarchical Generalized Linear Models (HGLMs)
Some Applications
RB Chap 10
Assign #5

Multivariate Extensions
Relationship with Structural Equations Modeling

RB Chap 6
Class Notes
4/21 Non-response and Missing Data Class Notes


Use of Sampling Weights Class Notes
4/28 -- 5/02 Final Exam – Friday May 2, 10 am -12 noon  

Course Requirements

Students should have completed CEP 933. CEP 934, a course on multivariate analysis, is a strong plus. Students who have not completed these courses must be comfortable with multiple regression, including the interpretation of output, basic formulas and conceptualization of calculations, statistical inferences, and applications to substantive issues.  Although knowledge of matrix algebra is not required as a prerequisite for the course, this notation simplifies the presentation of more complex multilevel models. YOU ARE RESPONSIBLE FOR ALL YOUR COMPUTING NEEDS.


Both SAS and HLM software will be used in this course.  SAS is available on most campus computers.  A student version of HLM can be downloaded for free from Scientific Software International (  If you would like the manual for the full version of HLM, you can order it from this website.

Grades & Grading Policy

Read the following very, very carefully:

Your grade, scored from 0 to 100, will be based on the performance of 5 homework assignments, and a final project/presentation, according to the following weights:

  Item  %
  Assignment 1  15
  Assignment 2  15
  Assignment 3  15
  Assignment 4  15
  Assignment 5  15
  Project/Presentation  25







Students are to work in groups of three, with membership determined by the end of week one. All assignments, and also the final project, are to reflect the "best-practices" of co-operative learning. Be sure to participate as an independent contributor, rather than a "sleeping partner" (business term). If you are not contributing in a constructive manner, fellow members have the obligation to inform the instructor of your situation as early as possible.

Print and submit your homework on time. Chronically late assignments or take-home exam will diminish their collective weight to be determined at the discretion of the instructor (we really do not want that).

The final project will consist of a 6-page (text, maximum) paper addressing a HLM analysis of a substantive nature that supports your group's in-class presentation. The presentation itself will be scheduled during the final exam-day for the class.  Various parts of the project will be due throughout the semester, with the paper and presentation due at the end of the course.  If you do not have a dataset for your project by the end of the third week, please consult the TA and the instructor for help. Note that the presentation itself counts for 60% and the paper to be submitted weighs about 40% towards the final project grade.

Letter grades are based on the following conversion from its original score.

 Score  Grade
 67-73  2.5
 74-83  3.0
 84-93  3.5
 94-100  4.0

How to do well:

  1. Allow at least 10 hours per assignment (more likely 15)
  2. Organize before you compute
  3. Follow examples in handouts
  4. Study with others
  5. Come to class!
  6. Be punctual -- this class can bury you if you get too far behind
  7. Be thorough -- respond to all parts of the questions
  8. Ask questions in class and come to office hours, attend labs, and review sessions
  9. IMPORTANT! Write clearly, be concise, and neat (print work, interspersed with hand-written equations, hand-sketched graphs, etc., is probably best.)

Attendance Policy

The TA will take attendance before each lecture. Punctuality is also a matter of courtesy. Send the TA a note if you know you are going to be absent, or be late.

University and Class Policies

  • Michigan State University seeks to ensure that its programs are accessible to all persons. Students in need of special assistance or an accommodation regarding any of the course requirements as outlined in the syllabus and discussed in class are advised to notify me immediately.  We will meet privately to discuss a resolution of your issue, which may or may not include an appropriate referral.  Confidentiality will be maintained regarding your special needs. To arrange for accommodation, students with disabilities should contact the Resource Center for People with Disabilities (RCPD), 353-9642.

  • Academic honesty:  academic dishonesty, including plagiarism, may result in a zero grade in the course and removal from the program.  If students are unclear about the Academic honesty policy, they are encouraged to consult the appropriate section in Spartan Life: Student Handbook and Resource Guide.  Please review again MSU's basic norms of academic honesty and integrity.

  • The instructor reserves the right to make any changes she considers academically advisable. Changes will be announced in class, it is your responsibility to keep up with any changed policies, schedules, and assignments.

  • You are responsible for any materials covered in classes that you miss.

IMPORTANT: The student, by taking the course, pledges adherence to the above said policies.

Teaching Assistant

Qiu Wang
Room/Hours TBD


Wednesdays (tentative)
Room/Hours TBD