Mixed and Hierarchical Linear Models

Mixed and Hierarchical Linear Models

This course will teach you the basic theory of linear and non-linear mixed effects models, hierarchical linear models, algorithms used for estimation, primarily for models involving normally distributed errors, and examples of data analysis.

This course will teach you the basic theory of linear and non-linear mixed effects models, hierarchical linear models, algorithms used for estimation, primarily for models involving normally distributed errors, and examples of data analysis.

$999 | Enroll Now
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Overview

This course explains the basic theory of linear and non-linear mixed-effects models, including hierarchical linear models (HLM). 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 when analyzing correlated data. The course provides a basic understanding and knowledge of mixed-effect models that will enable you to put what you learn into practice. You will use several software programs to fit mixed-effects models to real data sets; outcomes will be presented and discussed.

Intermediate/Advanced Level
4-Week Course
100% Online Courses
Expert Instructors
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Learning Outcomes

Students who complete this course will gain a basic understanding of mixed-effect models. They will use procedures in several software programs to fit mixed-effects models to real data sets. They will learn basic specifications of linear mixed effects models, techniques for estimation and hypothesis testing, and basic concepts of nonlinear mixed effects models. 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 the conceptual and theoretical material with practical solutions.

  • Specify a linear mixed model
  • Identify the associated marginal model
  • Estimate the covariance and fixed effect parameters
  • Conduct hypothesis tests on models
  • Estimate nonlinear mixed effects models

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.

Instructors

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Dr. James Hardin

Dr. James Hardin

Dr. James Hardin is an Associate Dean of Faculty Affairs and Curriculum Professor at the University of South Carolina. Co-author (with Joseph Hilbe) of Generalized Estimating Equations, Dr. Hardin is on the editorial board of The Stata Journal and is the developer of the Stata GEE command, and with Dr. Hilbe is the developer of the GLM command.

See Instructor Bio

Course Syllabus

Week 1

Overview of Linear Mixed Effects Models (LMM)

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

Week 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

Week 3

LMM Examples

  • Estimation
  • Hypothesis tests
  • Checking model assumptions

Week 4

Nonlinear Mixed Effects Models (NLMM): Basic Concepts

  • Estimation methods for NLMM
  • Applications of NLMM
  • Examples
  • Guided analysis of participant data sets

Class Dates

2023

Sep 22, 2023 to Oct 20, 2023

2024

Sep 20, 2024 to Oct 18, 2024

2025

No classes scheduled at this time.

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Prerequisites

The courses listed below are prerequisites for enrollment in this course:

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Introductory Statistics for College Credit

Matrix Algebra

This course will teach you the basics of vector and matrix algebra and operations necessary to understand multivariate statistical methods, including the notions of the matrix inverse, generalized inverse and eigenvalues and eigenvectors.
Topic: Statistics, Statistical Modeling | Skill: Intermediate | Credit Options: ACE, CAP, CEU
Class Start Dates: Aug 11, 2023, Mar 22, 2024, Aug 9, 2024
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Regression Analysis

This course will teach you how multiple linear regression models are derived, assumptions in the models, how to test whether data meets assumptions, and develop strategies for building and understanding useful models.
Topic: Statistics, Statistical Modeling | Skill: Intermediate | Credit Options: ACE, CAP, CEU
Class Start Dates: May 5, 2023, Oct 13, 2023, Jan 12, 2024

What Our Students Say​

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Peter Blenis

I certainly feel that I got my money's worth from this course and this was almost entirely due to the prompt, thoughtful and expert comments of Brady and Andrzej.

Peter Blenis
Professor Emeritus at University of Alberta
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The course will provide a solid background/springboard to my research in Longitudinal Data Analysis.  Questions which required participants to replicate examples in text consolidate learning very much! Instructors were on hand to answer every question that came their way.

June Simakani
Lecturer, Nelson Mandela Metropolitan University
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Frequently Asked Questions

Can I transfer or withdraw from a course?

We have a flexible transfer and withdrawal policy that recognizes circumstances may arise to prevent you from taking a course as planned. You may transfer or withdraw from a course under certain conditions.
  • Students are entitled to a full refund if a course they are registered for is canceled.
  • You can transfer your tuition to another course at any time prior to the course start date or the drop date, however a transfer is not permitted after the drop date.
  • Withdrawals on or after the first day of class are entitled to a percentage refund of tuition.
Please see this page for more information.

Who are the instructors at the Institute?

The Institute has more than 60 instructors who are recruited based on their expertise in various areas in statistics. Our faculty members are:

  • Authors of well-regarded texts in their area;
  • Advisory board members;
  • Senior faculty; and
  • Educators who have made important contributions to the field of statistics or online education in statistics.

The majority of our instructors have more than five years of teaching experience online at the Institute.

Please visit our faculty page for more information on each instructor at The Institute for Statistics Education.

Please see our knowledge center for more information.

What type of courses does the Institute offer?

The Institute offers approximately 80 courses each year. Topics include basic survey courses for novices, a full sequence of introductory statistics courses, bridge courses to more advanced topics. Our courses cover a range of topics including biostatistics, research statistics, data mining, business analytics, survey statistics, and environmental statistics.

Please see our course search or knowledge center for more information.

Do your courses have for-credit options?

Our courses have several for-credit options:

  • Continuing education units (CEU)
  • College credit through The American Council on Education (ACE CREDIT)
  • Course credits that are transferable to the INFORMS Certified Analytics Professional (CAP®)

Please see our knowledge center for more information.

Is the Institute for Statistics Education certified?

The Institute for Statistics Education is certified to operate by the State Council of Higher Education for Virginia (SCHEV). For more information visit: https://www.schev.edu/

Please see our knowledge center for more information.

Visit our knowledge base and learn more.

FAQs + Knowledge Base

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Additional Course Information

Organization of Course

This course takes place online 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.

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.

Time Requirements

This is a 4-week course requiring 10-15 hours per week of review and study, at times of your choosing.

Homework

Homework in this course consists of short answer questions to theoretical problems (some of which involve matrix algebra), guided data analysis problems using existing software, guided data modeling problems using existing software, and an end-of-course modeling project.

In addition to assigned readings, this course also has an end of course data modeling project, example software files, practice exercises, and supplemental readings available online.

Course Text

The course text is Linear Mixed Models: A Practical Guide using Statistical Software – third edition – by B. T. West, K. B. Welch, and A. T. Galecki, with contributions from B. W. Gillespie, which you can order online.

Please order a copy of your course textbook prior to course start 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).  Exercises should be doable with SAS, R, Stata, or SPSS.

Note:  If you are planning to use R in this course and are not already familiar with it, please consider taking one of our courses where R is introduced from the ground up:  “Introduction to R: Data Handling,”  “Introduction to R: Statistical Analysis,” or “Introduction to Modeling.”  R has a learning curve that is steeper than that of most commercial statistical software.

Software Uses and Descriptions | Available Free Versions
To learn more about the software used in this course, or how to obtain free versions of software used in our courses, please read our knowledge base article “What software is used in courses?” 

Course Fee & Information

Enrollment
Courses may fill up at any time and registrations are processed in the order in which they are received. Your registration will be confirmed for the first available course date unless you specify otherwise.

Transfers and Withdrawals
We have flexible policies to transfer to another course or withdraw if necessary.

Group Rates
Contact us to get information on group rates.

Discounts
Academic affiliation?  In most courses you are eligible for a discount at checkout.

New to Statistics.com?  Click here for a special introductory discount code.  

Invoice or Purchase Order
Add $50 service fee if you require a prior invoice, or if you need to submit a purchase order or voucher, pay by wire transfer or EFT, or refund and reprocess a prior payment.

Options for Credit and Recognition

This course is eligible for the following credit and recognition options:

No Credit
You may take this course without pursuing credit or a record of completion.

Mastery or Certificate Program Credit
If you are enrolled in mastery or certificate program that requires demonstration of proficiency in this subject, your course work may be assessed for a grade.

CEUs and Proof of Completion
If you require a “Record of Course Completion” along with professional development credit in the form of Continuing Education Units (CEU’s), upon successfully completing the course, CEU’s and a record of course completion will be issued by The Institute upon your request.

Supplemental Information

Literacy, Accessibility, and Dyslexia

At Statistics.com, we aim to provide a learning environment suitable for everyone. To help you get the most out of your learning experience, we have researched and tested several assistance tools. For students with dyslexia, colorblindness, or reading difficulties, we recommend the following web browser add-ons and extensions:

 

Chrome

 

Firefox

 

Safari

  • Navidys (for colorblindness, dyslexia, and reading difficulties)
  • HelperBird for Safari (for colorblindness, dyslexia, and reading difficulties)

Miscellaneous

There is no additional information for this course.

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Mixed and Hierarchical Linear Models
$999 | Enroll Now
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