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.
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
- 4 Weeks
- Expert Instructor
- Tuiton-Back Guarantee
- 100% Online
- TA Support
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.
Our Instructors
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
2022
Instructors:
2023
Instructors:
2024
Instructors:
Prerequisites
Private: Statistics 1 – Probability and Study Design
- Skill: Intermediate, Advanced
- Credit Options: CEU
Private: Statistics 2 – Inference and Association
- Skill: Intermediate, Advanced
- Credit Options: CEU
Matrix Algebra
- Skill: Intermediate, Advanced
- Credit Options: CEU
The Statistics.com courses have helped me a lot, pushing me to the limit and making me learn much more than I expected I could. The knowledge I gained I could immediately leverage in my job … then eventually led to landing a job in my dream company – Amazon.
Karolis Urbonas
This program has been a life and work game changer for me. Within 2 weeks of taking this class, I was able to produce far more than I ever had before.
Susan Kamp
The material covered in the Analytics for Data Science Certificate will be indispensable in my work. I can’t wait to take other courses. Great work!
Stephen McAllister
I learned more in the past 6 weeks than I did taking a full semester of statistics in college, and 10 weeks of statistics in graduate school. Seriously.
Amir Aminimanizani
This is the best online course I have ever taken. Very well prepared. Covers a lot of real-life problems. Good job, thank you very much!
Elena Rose
The more courses I take at Statistics.com, the more appreciation I have for the smart approach, quality of instructors, assistants, admin and program. Well done!
Leonardo Nagata
This course greatly benefited me because I am interested in working in AI. It has given me solid foundational knowledge…After completing this last course, I feel I have gained valuable skills that will enhance my employability in Data Science, opening up diverse career opportunities.
Richard Jackson
Frequently Asked Questions
-
What is your satisfaction guarantee and how does it work?
-
Can I transfer or withdraw from a course?
-
Who are the instructors at Statistics.com?
Visit our knowledge base and learn more.
Additional Information
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.
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.
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
- Color Enhancer (for colorblindness)
- HelperBird (for colorblindness, dyslexia, and reading difficulties)
Firefox
- Mobile Dyslexic
- Color Vision Simulation (native accessibility feature)
- Other native accessibility features instructions
Safari
- Navidys (for colorblindness, dyslexia, and reading difficulties)
- HelperBird for Safari (for colorblindness, dyslexia, and reading difficulties)