SAS for Mixed Models

Book Description

Discover the power of mixed models with SAS. Mixed models—now the mainstream vehicle for analyzing most research data—are part of the core curriculum in most master’s degree programs in statistics and data science. In a single volume, this book updates both SAS® for Linear Models, Fourth Edition, and SAS® for Mixed Models, Second Edition, covering the latest capabilities for a variety of applications featuring the SAS GLIMMIX and MIXED procedures. Written for instructors of statistics, graduate students, scientists, statisticians in business or government, and other decision makers, SAS® for Mixed Models is the perfect entry for those with a background in two-way analysis of variance, regression, and intermediate-level use of SAS.

This book expands coverage of mixed models for non-normal data and mixed-model-based precision and power analysis, including the following topics:
  • Random-effect-only and random-coefficients models
  • Multilevel, split-plot, multilocation, and repeated measures models
  • Hierarchical models with nested random effects
  • Analysis of covariance models
  • Generalized linear mixed models
This book is part of the SAS Press program.

Table of Contents

  1. About This Book
  2. Dedication and Acknowledgments
  3. Chapter 1: Mixed Model Basics
    1. 1.1 Introduction
    2. 1.2 Statistical Models
    3. 1.3 Forms of Linear Predictors
    4. 1.4 Fixed and Random Effects
    5. 1.5 Mixed Models
    6. 1.6 Typical Studies and Modeling Issues That Arise
    7. 1.7 A Typology for Mixed Models
    8. 1.8 Flowcharts to Select SAS Software to Run Various Mixed Models
  4. Chapter 2: Design Structure I: Single Random Effect
    1. 2.1 Introduction
    2. 2.2 Mixed Model for a Randomized Block Design
    3. 2.3 The MIXED and GLIMMIX Procedures to Analyze RCBD Data
    4. 2.4 Unbalanced Two-Way Mixed Model: Examples with Incomplete Block Design
    5. 2.5 Analysis with a Negative Block Variance Estimate: An Example
    6. 2.6 Introduction to Mixed Model Theory
    7. 2.7 Summary
  5. Chapter 3: Mean Comparisons for Fixed Effects
    1. 3.1 Introduction
    2. 3.2 Comparison of Two Treatments
    3. 3.3 Comparison of Several Means: Analysis of Variance
    4. 3.4 Comparison of Quantitative Factors: Polynomial Regression
    5. 3.5 Mean Comparisons in Factorial Designs
    6. 3.6 Summary
  6. Chapter 4: Power, Precision, and Sample Size I: Basic Concepts
    1. 4.1 Introduction
    2. 4.2 Understanding Essential Background for Mixed Model Power and Precision
    3. 4.3 Computing Precision and Power for CRD: An Example
    4. 4.4 Comparing Competing Designs I—CRD versus RCBD: An Example
    5. 4.5 Comparing Competing Designs II—Complete versus Incomplete Block Designs: An Example
    6. 4.6 Using Simulation for Precision and Power
    7. 4.7 Summary
  7. Chapter 5: Design Structure II: Models with Multiple Random Effects
    1. 5.1 Introduction
    2. 5.2 Treatment and Experiment Structure and Associated Models
    3. 5.3 Inference with Factorial Treatment Designs with Various Mixed Models
    4. 5.4 A Split-Plot Semiconductor Experiment: An Example
    5. 5.5 A Brief Comment about PROC GLM
    6. 5.6 Type × Dose Response: An Example
    7. 5.7 Variance Component Estimates Equal to Zero: An Example
    8. 5.8 A Note on PROC GLM Compared to PROC GLIMMIX and PROC MIXED: Incomplete Blocks, Missing Data, and Spurious Non-Estimability
    9. 5.9 Summary
  8. Chapter 6: Random Effects Models
    1. 6.1 Introduction: Descriptions of Random Effects Models
    2. 6.2 One-Way Random Effects Treatment Structure: Influent Example
    3. 6.3 A Simple Conditional Hierarchical Linear Model: An Example
    4. 6.4 Three-Level Nested Design Structure: An Example
    5. 6.5 A Two-Way Random Effects Treatment Structure to Estimate Heritability: An Example
    6. 6.6 Modern ANOVA with Variance Components
    7. 6.7 Summary
  9. Chapter 7: Analysis of Covariance
    1. 7.1 Introduction
    2. 7.2 One-Way Fixed Effects Treatment Structure with Simple Linear Regression Models
    3. 7.3 One-Way Treatment Structure in an RCB Design Structure—Equal Slopes Model: An Example
    4. 7.4 One-Way Treatment Structure in an Incomplete Block Design Structure: An Example
    5. 7.5 One-Way Treatment Structure in a BIB Design Structure: An Example
    6. 7.6 One-Way Treatment Structure in an Unbalanced Incomplete Block Design Structure: An Example
    7. 7.7 Multilevel or Split-Plot Design with the Covariate Measured on the Large-Size Experimental Unit or Whole Plot: An Example
    8. 7.8 Summary
  10. Chapter 8: Analysis of Repeated Measures Data
    1. 8.1 Introduction
    2. 8.2 Mixed Model Analysis of Data from Basic Repeated Measures Design: An Example
    3. 8.3 Covariance Structures
    4. 8.4 PROC GLIMMIX Analysis of FEV1 Data
    5. 8.5 Unequally Spaced Repeated Measures: An Example
    6. 8.6 Summary
  11. Chapter 9: Best Linear Unbiased Prediction (BLUP) and Inference on Random Effects
    1. 9.1 Introduction
    2. 9.2 Examples Motivating BLUP
    3. 9.3 Obtainment of BLUPs in the Breeding Random Effects Model
    4. 9.4 Machine-Operator Two-Factor Mixed Model
    5. 9.6 Matrix Notation for BLUP
    6. 9.7 Summary
  12. Chapter 10: Random Coefficient Models
    1. 10.1 Introduction
    2. 10.2 One-Way Random Effects Treatment Structure in a Completely Randomized Design Structure: An Example
    3. 10.3 Random Student Effects: An Example
    4. 10.4 Repeated Measures Growth Study: An Example
    5. 10.5 Prediction of the Shelf Life of a Product
    6. 10.6 Summary
  13. Chapter 11: Generalized Linear Mixed Models for Binomial Data
    1. 11.1 Introduction
    2. 11.2 Three Examples of Generalized Linear Mixed Models for Binomial Data
    3. 11.3 Example 1: Binomial O-Ring Data
    4. 11.4 Generalized Linear Model Background
    5. 11.5 Example 2: Binomial Data in a Multicenter Clinical Trial
    6. 11.6 Example 3: Binary Data from a Dairy Cattle Breeding Trial
    7. 11.7 Summary
  14. Chapter 12: Generalized Linear Mixed Models for Count Data
    1. 12.1 Introduction
    2. 12.2 Three Examples Illustrating Generalized Linear Mixed Models with Count Data
    3. 12.3 Overview of Modeling Considerations for Count Data
    4. 12.4 Example 1: Completely Random Design with Count Data
    5. 12.5 Example 2: Count Data from an Incomplete Block Design
    6. 12.6 Example 3: Linear Regression with a Discrete Count Dependent Variable
    7. 12.7 Blocked Design Revisited: What to Do When Block Variance Estimate is Negative
    8. 12.8 Summary
  15. Chapter 13: Generalized Linear Mixed Models for Multilevel and Repeated Measures Experiments
    1. 13.1 Introduction
    2. 13.2 Two Examples Illustrating Generalized Linear Mixed Models with Complex Data
    3. 13.3 Example 1: Split-Plot Experiment with Count Data
    4. 13.4 Example 2: Repeated Measures Experiment with Binomial Data
  16. Chapter 14: Power, Precision, and Sample Size II: General Approaches
    1. 14.1 Introduction
    2. 14.2 Split Plot Example Suggesting the Need for a Follow-Up Study
    3. 14.3 Precision and Power Analysis for Planning a Split-Plot Experiment
    4. 14.4 Use of Mixed Model Methods to Compare Two Proposed Designs
    5. 14.5 Precision and Power Analysis: A Repeated Measures Example
    6. 14.6 Precision and Power Analysis for Non-Gaussian Data: A Binomial Example
    7. 14.7 Precision and Power: Example with Incomplete Blocks and Count Data
    8. 14.8 Summary
  17. Chapter 15: Mixed Model Troubleshooting and Diagnostics
    1. 15.1 Introduction
    2. 15.2 Troubleshooting
    3. 15.3 Residuals
    4. 15.4 Influence Diagnostics
    5. 15.5 Two Diagnostic Plots Useful for Non-Gaussian Data
    6. 15.5 Summary
  18. Appendix A: Linear Mixed Model Theory
    1. A.1 Introduction
    2. A.2 Matrix Notation
    3. A.3 Formulation of the Mixed Model
    4. A.4 Estimating Parameters, Predicting Random Effects
    5. A.5 Statistical Properties
    6. A.6 Model Selection
    7. A.7 Inference and Test Statistics
  19. Appendix B: Generalized Linear Mixed Model Theory
    1. B.1 Introduction
    2. B.2 Formulation of the Generalized Linear Model
    3. B.3 Formulation of the Generalized Linear Mixed Model
    4. B.4 Conditional versus Marginal Models and Inference Space
    5. B.5 Integral Approximation
  20. References
  21. Index

Product Information

  • Title: SAS for Mixed Models
  • Author(s): Walter W. Stroup, George A. Milliken, Elizabeth A. Claassen, Russell D. Wolfinger
  • Release date: December 2018
  • Publisher(s): SAS Institute
  • ISBN: 9781635261523