TITLE: Working with Generalized Linear and Nonlinear Mixed Models
INSTRUCTOR: Professor Walter Stroup, The University of Nebraska-Lincoln
MODERATOR: Alfred H. Balch


This course surveys mixed model concepts and methods with a focus on experiments with “mixed model issues” – e.g. various forms of clustering, including repeated measures, split-plot and multi-location studies – in conjunction with “generalized model” issues, i.e. non-Gaussian response variables. Linear and non-linear mixed models are included.

Day One will emphasize essential background ideas and methodology. We start with a survey of the various types of mixed models. We discuss overarching issues that confront analysts who work with correlated, non-normal data, such as overdispersion, marginal and conditional models. We present the various estimation methods for mixed models, and what we have learned to date about their advantages and disadvantages. Examples will be used to illustrate concepts and methods.

Day Two will focus primarily on mixed model applications and on issues associated with these applications. Additional supporting theory will be introduced as needed. We focus both on methods applicable to all mixed models as well as considerations uniquely applicable to specific distribution-model combinations, bearing in mind that different types of data and the different models present particular challenges. Examples will illustrate the difference between pseudo-likelihood and integral approximation estimation algorithms, and when each is preferable. Examples will illustrate the difference between marginal and conditional inference. We will include a “gentle” introduction to Bayesian estimation and inference, and discuss differences between Bayesian and frequentist inference. Time permitting, we will discuss additional issues including model selection, model averaging, mixed model-based precision and power analysis, and the use of mixed models for prediction.

Computations will use the mixed model tools in SAS/STAT, primarily the GLIMMIX, NLMIXED and MCMC procedures. No R examples will be presented, but R packages analogous to SAS mixed model procedures will be noted where relevant. The principles in this course should be applicable to any mixed model-capable software. Attendees should have background in statistical design and associated statistical analysis.


  1. Mixed Model Basics
    1. A General Setting for Statistical Modeling
    2. Types of Mixed Models
  1. Case 1 – Gaussian (normal) data – linear and nonlinear mixed models (LMM and NLMM)
  2. Case 2 – non-Gaussian data – generalized mixed models (GLMM and GNLMM)
    1. Marginal versus Conditional Models
  1. Modeling Issues
    1. Translating Data (design) Structure to Appropriate Model
  1. Aspect 1 – Model as Characterization of How Data Arise
  2. Aspect 2 – Model as Template for Analysis
    1. Design-Induced Issues
  1. Overdispersion
  2. Within Subject Correlation
    1. Distributional Issues: Likelihood and Quasi-Likelihood
  1. Estimation and Inference
    1. Maximum Likelihood and Residual Maximum Likelihood
    2. Three Estimation Methods
  1. Frequentist Method 1: pseudo-likelihood
  2. Frequentist Method 2: integral approximation (Laplace and quadrature)
  • Bayesian methods: MCMC, etc.
    1. Estimable and Predictable Functions
    2. Inference Approaches
  1. Frequentist
  2. Bayesian
  1. Example Applications 1 – Gaussian (normally distributed) Data
    1. Intro example – paired comparison
    2. Multi-Level Design
    3. Repeated Measures
    4. Nonlinear and Smoothing Spline Mixed Models
  2. Example Applications 2 – Count Data
    1. Distributions – focus on Poisson and negative binomial
    2. Intro Example: Blocked Design
    3. Repeated Measures with Counts
    4. Too many zeroes: Zero-inflated and Hurdle Models
    5. Gentle intro to Bayes: Poisson-normal and Poisson-gamma models
  3. Example Applications 3 – Proportions
    1. Discrete proportions
  1. Binary
  2. Binomial
  • Multinomial
    1. Continuous Proportions
    2. Beta hurdle models
    3. Gentle intro to Bayes continued – Beta-binomial model
  1. Additional Issues
    1. Model selection and model averaging
    2. Using Mixed Models for Planning
  1. Mixed Model Precision and Power Analysis
  2. Comparing Competing Designs using mixed model tools
    1. Inference Issues: Estimation, Hypothesis Testing and Prediction

Instructor’s Bio:

Walt Stroup is Emeritus Professor of Statistics at the University of Nebraska-Lincoln. He served on the University of Nebraska faculty from 1979 until 2020. His responsibilities included teaching statistical modeling, design of experiments, and research specializing in mixed models and their applications in agriculture, natural resources, medical and pharmaceutical sciences, education, and the behavioral sciences. He is the founding chair of Nebraska’s Department of Statistics, and served as chair from 2001 until 2010. In 2020, he received the University of Nebraska’s Outstanding Teaching and Innovative Curriculum Award, the university’s highest teaching honor. He was a member of PQRI’s Stability Shelf-Life Working Group from its inception in 2006 until its disbanding in 2019. He received PQRI’s Excellence in Research award in 2009. He co-authored SAS for Mixed Models, SAS for Linear Models, 4th ed., and authored Generalized Linear Mixed Models: Modern Concepts, Methods and Applications. He has conducted numerous short courses on mixed and generalized linear models for industry and professional organizations in Africa, Europe, Australia and North America. He is a Fellow of the American Statistical Association.

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