Generalized Linear Mixed Models

Walt Stroup is an Emeritus Professor of Statistics. He served on the University of Nebraska statistics faculty for over 40 years, specializing in statistical modeling and statistical design. He is a Fellow of the American Statistical Association, winner of the University of Nebraska Outstanding Teaching and Innovative Curriculum Award and author or co-author of three books on mixed models and their extensions.Marina Ptukhina (Pa-too-he-nuh), PhD, is an Associate Professor of Statistics at Whitman College. She is interested in statistical modeling, design and analysis of research studies and their applications. Her research includes applications of statistics to economics, biostatistics and statistical education. Ptukhina earned a PhD in Statistics from the University of Nebraska-Lincoln, a Master of Science degree in Mathematics from Texas Tech University and a Specialist degree in Management from The National Technical University "Kharkiv Polytechnic Institute."Julie Garai, PhD, is a Data Scientist at Loop. She earned her PhD in Statistics from the University of Nebraska-Lincoln and a bachelor’s degree in Mathematics and Spanish from Doane College. Dr Garai actively collaborates with statisticians, psychologists, ecologists, forest scientists, software engineers, and business leaders in academia and industry. In her spare time, she enjoys leisurely walks with her dogs, dance parties with her children and playing the trombone.

"This is an excellent textbook on GLMMs. It provides a unified framework for GLMMs by extending linear models to GLMMs and redefining them with fixed and random effects for Gaussian and non-Gaussian response variables. It will be of great interest to graduate students in statistics and practitioners who have a background in classical linear and generalized linear models and would like to learn about GLMMs. Although this book focuses on SAS as a learning tool, the topics will also be beneficial to non-SAS users. Due to its in-depth coverage, it will be an invaluable resource for those who would like to apply the methodology of GLMMs and conduct analysis in their research."- Xing Liu, Journal of the American Statistical Association, May 2025

• Preface to the Second EditionPart 1: Essential Background1. Modeling Basics2. Design Matters3. Setting the StagePart 2: Estimation and Inference Theory4. Pre-GLMM Estimation and Inference Basics5. GLMM Estimation6. Inference, Part I7. Inference, Part IIPart 3: Applications8. Treatment and Explanatory Variable Structure9. Multi-Level Models10. Best Linear Unbiased Prediction11. Counts12. Rates and Proportions13. Zero-inflated and Hurdle Models14. Multinomial Data15. Time-to-Event Data16. Smoothing Splines and Additive Models17. Correlated Errors, part 1: Repeated Measures18. Correlated Errors, part 2: Spatial Variability19. Bayesian Implementation of GLMM20. Four Bayesian GLMM Examples21. Precision, Power, Sample Size and Planning