EPSY 512 - Hierarchical Linear Models

Semester: Spring 2008	Professor: George Karabatsos
Time: Mondays 5:00-8:00pm	Phone: 312-413-1816
Room: 2217 EPASW	E-mail: georgek@uic.edu
Office Hours: Mon 2-4 (EPASW 1034)	CRN: 26329

Course Description:
This course introduces students to Hierarchical Linear Models, which provide an important linear mixed-model that is widely applicable for research areas of education, psychology, medicine, and other fields.
A Hierarchical Linear Model (HLM) has a nested structure that allows effects to vary from one context to another. For example, in educational research, a Hierarchical Linear Model is often used to analyze data about student math achievement. Here, students are nested within schools, and the model permits the investigation of the relationship between student socioeconomic status and math achievement, by school, and allows the investigation of school-level factors that affect this relationship. To give another example, for longitudinal data analysis, the HLM provides an approach to learn the growth curve of each individual subject, and also provide a way to identify the subject-level predictor variables that significantly predict changes in the subjects' growth curves.
More generally, the HLM provides a single flexible framework for statistical modeling that applies to many important tasks of data analysis, including:
(1) analysis of variance (ANOVA), analysis of covariance (ANCOVA),
(2) random-coefficients regression analysis,
(3) categorical data analysis,
(4) longitudinal (repeated-measures) analysis,
(5) meta-analysis, and
(6) psychometric analysis with predictor variables (Rasch model, FACETS model, etc.).
This course will present various Hierarchical Linear Models from both a Bayesian and a frequentist perspective of statistical inference.
Moreover, this course will also present semiparametric Hierarchical Linear Models, which a way to circumvent the parametric assumptions of "off-the-shelf" versions of Hierarchical Linear Models (namely, normality of error distribution, normality of random effects, and the link function being defined by the standard logistic distribution), assumptions which may be overly-restrictive for data sets.
Finally, all Hierarchical Linear Models discussed in the course will be illustrated on data sets arising from education, psychology, medicine, and other fields.
Furthermore, through in-class exercises (which count as credit towards two open-notes tests), students will learn how to perform data analysis with Hierarchical Linear Models using the HLM and R software (DPpackage), and will give a 25 minute presentation about a practical implementation of a hierarchical linear model on data.

Prerequisites:
EPSY 547 - Multiple Regression in Educational Research,
or
EPSY 563 - Advanced Analysis of Variance In Educational Research,
or equivalents,
or consent.

Textbooks:
Raudenbush, S., & Bryk, A.S. (2002). Hierarchical Linear Models: Applications and Data Analysis Methods. Sage. (ISBN 0-7619-1904-X)
Raudenbush, S., Bryk, A., Cheong, Y.-F., & Congdon, R. (2004). HLM 6: Hierarchical Linear and Nonlinear modeling. Lincolnwood, IL: Scientific Software International. (ISBN 0-89498-054-8)

These textbooks can be ordered through the Chicago textBook bookstore, on 1076 W Taylor St.
These books may be purchased at a lower proce through Scientific Software International.

Key Foundational Articles:
Breslow, N.E., and Clayton, D. (1993). Approximate inference in generalized linear mixed models. Journal of the American Statistical Association, 88, 9-25.
Kleinman K., & Ibrahim J.G. (1998) A Semi-Parametric Bayesian Approach to the Random Effects Model. Biometrics, 54, 921-938.
Kleinman, K.P. & Ibrahim, J.G. (1998). A semiparametric Bayesian approach to generalized linear mixed models. Statistics In Medicine, 17, 2579-2596.
Laird, N.M., & Ware, J.H. (1982). Random-effects models for longitudinal data. Biometrics, 38, 963-974.
Lindley, D.V., & Smith, A.F.M. (1972). Bayes estimates for the linear model. Journal of the Royal Statistical Society Ser. B, 34, 1-41.
Nelder, J.A., & Wedderburn, R.W.M. (1972). Generalized Linear Models. Journal of the Royal Statistical Society, Series A, 135, 370-384.
Zeger, S.L., & Karim, M.R. (1991). Generalized linear models with random effects: A Gibbs sampling approach. Journal of the American Statistical Association, 86, 79-86.

COURSE SCHEDULE

Date	Topic	Read
Jan14	Assignments/tasks. Introduction and motivation for Hierarchical Linear Models. Foundations: Review of Basic Probability Theory ----- Sample Space (countable and uncountable), Random Variable, Borel sigma-algebra ----- Axioms of Probability, Statistical Independence, Mutual Independence ----- Conditional Probability, Bayes Theorem, Conditional Independence	Notes, RB1
21	Martin Luther King' Birthday (no class)
28	Foundations: Random Variables And Their Distributions ----- Cumulative distribution function (cdf) ----- Discrete random variable, discrete distribution, and probability mass function (pmf) ----- Continuous random variable, Continuous distribution, and probability density function ----- Basics of Integration -- Summarizing a Distribution Probability Models -- Definition of a Probability Model ----- Definition of a Parametric Model, Nonparametric Model, semiparametric Model, and a Hierarchical (Mixture) Model ----- Connection between Linear Mixed Models and Hierarchical Linear Models	Notes; RB2, RB3
Feb4	Foundations: Applying Probability Models for Data Analysis -- Inference With a Probability Model ----- Frequentist statistical inference, and Bayesian statistical inference ----- Point-estimation of a parameter -------- M-estimation, Maximum-likelihood estimation, Marginal maximum likelihood estimation -------- Inferential Processes for linear models, generalized linear models, and parametric and semiparametric HGLMs ----- Bayes Theorem, prior distribution, and inference of the posterior distribution ----- Markov Chain Monte Carlo (MCMC) methods of generating samples from the posterior distribution.	RB4, DPpack HLM manual
11	HLM and Semiparametric HLM: One-way random-effects ANOVA, ANCOVA, ordinary linear regression, Random Coefficients regression Data Sets Analyzed: (1) Blood coagulation time (in seconds) for four different diets, (2) Math achievement in elementary schools.	RB5,8 M3,4 DPpack HLM manual
18	HLM and Semiparametric HLM: Means-as-outcomes model, model for non-random varying slopes, and Full HLM model Data Sets Analyzed: (1) Math achievement data, (2) forecasting presidential elections, (3) 3-level HLM, math achievement (students nested within classrooms nested within schools) (4) Australian Institute of Sport data	RB6 DPpack HLM manual
25	HLM and Semiparametric HLM for Repeated Measures and longitudinal analysis Data Sets Analyzed: (1) Repeated Calcium measurements of dominant ulna bone in older women, (2) Efficacy of weight loss program, (3) National Youth Survey (NYS) (teens' attitudes about deviant behavior)	RB7 DPpack HLM manual
Mar3	HLM and Semiparametric HLM for Meta-Analysis Data Sets Analyzed: (1) Effects of coaching program on SAT-V scores, over 8 different experiments (schools), (2) Rat Tumor data, (3) Beta-Blocker data Midterm Exam Is Due	RB10 M5,6 DPpack HLM manual
10	Generalized HLM and Semiparametric HLM, for, binary, binomial, and counts as outcomes. Data Sets Analyzed: (1) Student dropout rate among schools in Thailand (binomial outcomes, GTHAI1.sav, THAI2.sav), (2) Bernoulli (dichotomous) outcomes (UTHAI1.sav), (3) Respiratory Data, (4) Math Achievement Data, (5) Rat Tumor Data, (6) Bioassay Data Example, (7) Prostate cancer data example. (8) Reaction time data (modelled as Poisson counts), (9) Weight Loss Data (10) Schizophrenia Data	DPpack HLM manual
17	Generalized HLM and Semiparametric HLM, for ordered-category outcomes, and models for unordered category outcomes. Data Sets Analyzed: (1) Analysis of teachers' contexts in high schools (TCHR1.sav, TCHR2.sav), (2) Association between health and religious membership, by employment status	DPpack HLM manual
24	*SPRING BREAK*
31	HLM and Semiparametric HLM for Psychometric Analysis Data Sets Analyzed: (1) Rasch analysis of math exam (MathL1.sav, MathL2.sav), (2) Rasch item bias analysis of Knox Cube Test, (3) Rasch analysis of rating scale questionnaire (Liking For Science), (4) ETS data; analysis of examinee's performance on on essays, as rated by judges (5) National Assessments of Educational Progress, Reading Test	RB11 DPpack HLM manual
Apr7	Student Presentations
14	Student Presentations
21	Student Presentations
28	Student Presentations
May5	FINAL EXAM WEEK Final Exam is due (Please leave final exams in my mailbox in Room 3233)

Grading Policy:
Both take-home exams, together, are worth 70% of the final grade, and the Final presentation is worth 30% of the final grade. Final grades will be given out according to the following scale:

A	90% - 100%
B	79% - 89%
C	68% - 78%
D	57% - 67%
F	56% - Lower

Students will spend substantial amounts of time reading, and on the computer. It is assumed that students will exert individual initiative in solving computing/analysis problems as they arise.
(Standard policy: There are no exceptions to the above grading scale, and no extra credit work will be accepted. Incompletes will be considered only for students with extenuating circumstances. Poor performance on assignments will not be considered in a request for an incomplete).

Data Analyses Presentation:
The presentation, which should be 25 minutes in length (about 15 PowerPoint slides), will deal with an application of a parametric or semiparametric HLM on a real data set. The presentation should (at least) include:

Introduction -
Describe in detail the substantive problem you will be solving in this research study,
and the rationale/theory underpinning the data you will analyze (10 points).

Methods -
Describe sample characteristics (5 points).
Fully describe the HLM model you will use to answer your research questions
(using words and mathematical notation), and include a discussion of the assumptions of your model. (10 points)
Which parameters will you interpret to answer your research questions? (10 points)

Results -
Fully describe the results of your HLM model, including all significant and non-significant effects
at Level 1 and Level 2 of the model. (25 points)

Discussion -
What are the implications of the results of your study, and potential future directions with this research (10 points).

Everyone starts with 70 points. I will deduct points from each section if you incorrectly interpret your results, fail to report/describe or fail to fully report/describe any of the information we have covered in class that is relevant to your particular investigation.

Disability Services:
UIC strives to ensure the accessibility of programs, classes, and services to students with disabilities. Reasonable accommodations can be arranged for students with various types of disabilities, such as documented learning disabilities, vision, or hearing impairments, and emotional or physical disabilities. If you need accommodations for this class, please let your instructor know your needs and he/she will help you obtain the assistance you need in conjunction with the Office of Disability Services (1190 SSB, 413-2183).