Mixed and Hierarchical Linear Models

taught by Andrzej Galecki

Brief Description:

This course will explain the basic theory of linear and non-linear mixed effects models, including hierarchical linear models. It will outline the algorithms used for estimation, primarily for models involving normally distributed errors, and will provide examples of data analysis. The course aims at providing a basic understanding and knowledge of the mixed effect models that will allow you to use them in practice.

Instructor(s):
Level: Advanced-Intermediate

Who Should Take This Course:

Researchers analyzing longitudinal or clustered data sets arising from experiments, clinical trials, or surveys, where the data are not amenable to simple statistical analysis and correlated observations need to be accounted for.

Dates:
May 10, 2013 to June 07, 2013
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Registration:
Please read the syllabus tab, noting the prerequisites, text and software requirements.

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Mixed and Hierarchical Linear Models

taught by Andrzej Galecki

Aim of Course:

This course will explain the basic theory of linear and non-linear mixed effects models, including hierarchical linear models (HLM). It will outline the algorithms used for estimation, primarily for models involving normally distributed errors, and will provide examples of data analysis. The course aims at providing a basic understanding and knowledge of the mixed effect models that will allow you to use them in practice. To achieve this aim, the use of procedures in R and SAS to fit mixed effects models to real data sets will be presented and discussed. The instructors will also demonstrate model fitting using other procedures as requested.

Mixed models are a powerful class of models used for the analysis of correlated data. Examples of correlated data include, but are not limited to, clustered data, repeated observations, longitudinal data, multiple dependent variables, spatial data or data from population pharmacokinetic/pharmacodynamic studies. A key feature of mixed models is that, by introducing random effects in addition to fixed effects, they allow you to address multiple sources of variation, e.g. in the longitudinal study they allow you to take into account both within- and between- subject variation.

The course will detail a basic theory of mixed models and will provide an overview of estimation methods, with emphasis on the linear case. Concepts of mixed models will be illustrated with examples analyzed using PROC/MIXED in SAS and functions in R. Most of the illustrations can also be done in Stata and/or SPSS (not all features are available in those packages, and the instructor is not familiar with them). Participants are strongly encouraged to contribute to discussions on the online course discussion board, where exchanges of examples, software code, and ideas about modeling approaches enhance conceptual and theoretical material with practical solutions.

Prerequisite(s):

• Introduction to Statistics courses, 1-3
• Regression Analysis
• Matrix Algebra

Course Program:

SESSION 1: Overview of Linear Mixed Effects Models (LMM)

• Specification of LMM
• The Marginal Model Implied by a LMM

SESSION 2: Estimation and Hypothesis Tests in LMMs

• Estimation of Covariance Parameters (ML vs REML estimation)
• Estimation of Fixed Effect Parameters
• Wald and likelihood ratio tests

SESSION 3: LMM Examples

• Estimation
• Hypothesis tests
• Checking model assumptions

SESSION 4: Nonlinear Mixed Effects Models (NLMM): Basic Concepts

• Estimation methods for NLMM
• Applications of NLMM
• Examples

HOMEWORK:

Homework in this course consists of short answer questions to test concepts, guided data analysis problems using software, guided data modeling problems using software, and end of course data modeling project.

Organization of the Course:

This course takes place over the internet at the Institute for 4 weeks. During each course week, you participate at times of your own choosing - there are no set times when you must be online. Course participants will be given access to a private discussion board. In class discussions led by the instructor, you can post questions, seek clarification, and interact with your fellow students and the instructor.

The course typically requires 15 hours per week. At the beginning of each week, you receive the relevant material, in addition to answers to exercises from the previous session. During the week, you are expected to go over the course materials, work through exercises, and submit answers. Discussion among participants is encouraged. The instructor will provide answers and comments, and at the end of the week, you will receive individual feedback on your homework answers.

Credit:
Students come to the Institute for a variety of reasons. As you begin the course, you will be asked to specify your category:

1. You may be interested only in learning the material presented, and not be concerned with grades or a record of completion.
2. You may be enrolled in PASS (Programs in Analytics and Statistical Studies) that requires demonstration of proficiency in the subject, in which case your work will be assessed for a grade.
3. You may require a "Record of Course Completion," along with professional development credit in the form of Continuing Education Units (CEU's).  For those successfully completing the course, 5.0 CEU's and a record of course completion will be issued by The Institute, upon request.

Course Text:

The course text is Linear Mixed Models: A Practical Guide using Statistical Software by B. T. West, K. B. Welch, and A. T. Galecki, with contributions from B. W. Gillespie, which you can order from CRC Press, or by using this form. CRC Press typically gives students a generous discount when students order the text using the above form (not by ordering the text online).

PLEASE ORDER YOUR COPY IN TIME FOR THE COURSE STARTING DATE.

 

Software:

Concepts of mixed models will be illustrated with examples analyzed using PROC/MIXED in SAS and functions in R. Most of the illustrations for the linear case will have parallel examples in Stata and/or SPSS (not all features are available in those packages), but instructor is familiar only with SAS and R.  TA can provide some help with Stata; no help is available for SPSS.  Exercises should be doable with SAS, R, Stata, or SPSS. For information on obtaining software, click here.

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Mixed and Hierarchical Linear Models

taught by Andrzej Galecki

Instructor(s):
Dates:
May 10, 2013 to June 07, 2013
Course Fee: $499
Academic Rate: $399

Before registering, please read the syllabus tab, noting the prerequisites, text and software requirements. When you click the register button, you will be taken to our secure transaction page.

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