SAS for Mixed Models, Second Edition, 2nd Edition

SAS for Mixed Models, Second Edition, 2nd Edition

by Ramon C. Littell, George A. Milliken, Walter W. Stroup, Russell D. Wolfinger, Oliver Schabenberger
Released June 2007
Publisher(s): SAS Institute
ISBN: 9781599940786

Read it now on the O’Reilly learning platform with a 10-day free trial.

O’Reilly members get unlimited access to books, live events, courses curated by job role, and more from O’Reilly and nearly 200 top publishers.

Start your free trial

Book description


The indispensable, up-to-date guide to mixed models using SAS. Discover the latest capabilities available for a variety of applications featuring the MIXED, GLIMMIX, and NLMIXED procedures in SAS for Mixed Models, Second Edition, the comprehensive mixed models guide for data analysis, completely revised and updated for SAS 9 by authors Ramon Littell, George Milliken, Walter Stroup, Russell Wolfinger, and Oliver Schabenberger. The theory underlying the models, the forms of the models for various applications, and a wealth of examples from different fields of study are integrated in the discussions of these models: random effect only and random coefficients models; split-plot, multilocation, and repeated measures models; hierarchical models with nested random effects; analysis of covariance models; spatial correlation models; generalized linear mixed models; and nonlinear mixed models.

Professionals and students with a background in two-way ANOVA and regression and a basic knowledge of linear models and matrix algebra will benefit from the topics covered.

This book is part of the SAS Press program.

Table of contents

  1. Preface
  2. Chapter 1 Introduction
    1. 1.1 Types of Models That Produce Data
    2. 1.2 Statistical Models
    3. 1.3 Fixed and Random Effects
    4. 1.4 Mixed Models
    5. 1.5 Typical Studies and the Modeling Issues They Raise
    6. 1.6 A Typology for Mixed Models
    7. 1.7 Flowcharts to Select SAS Software to Run Various Mixed Models
  3. Chapter 2 Randomized Block Designs
    1. 2.1 Introduction
    2. 2.2 Mixed Model for a Randomized Complete Blocks Design
    3. 2.3 Using PROC MIXED to Analyze RCBD Data
    4. 2.4 Introduction to Theory of Mixed Models
    5. 2.5 Example of an Unbalanced Two-Way Mixed Model: Incomplete Block Design
    6. 2.6 Summary
  4. Chapter 3 Random Effects Models
    1. 3.1 Introduction: Descriptions of Random Effects Models
    2. 3.2 Example: One-Way Random Effects Treatment Structure
    3. 3.3 Example: A Simple Conditional Hierarchical Linear Model
    4. 3.4 Example: Three-Level Nested Design Structure
    5. 3.5 Example: A Two-Way Random Effects Treatment Structure to Estimate Heritability
    6. 3.6 Summary
  5. Chapter 4 Multi-factor Treatment Designs with Multiple Error Terms
    1. 4.1 Introduction
    2. 4.2 Treatment and Experiment Structure and Associated Models
    3. 4.3 Inference with Mixed Models for Factorial Treatment Designs
    4. 4.4 Example: A Split-Plot Semiconductor Experiment
    5. 4.5 Comparison with PROC GLM
    6. 4.6 Example: Type × Dose Response
    7. 4.7 Example: Variance Component Estimates Equal to Zero
    8. 4.8 More on PROC GLM Compared to PROC MIXED: Incomplete Blocks, Missing Data, and Estimability
    9. 4.9 Summary
  6. Chapter 5 Analysis of Repeated Measures Data
    1. 5.1 Introduction
    2. 5.2 Example: Mixed Model Analysis of Data from Basic Repeated Measures Design
    3. 5.3 Modeling Covariance Structure
    4. 5.4 Example: Unequally Spaced Repeated Measures
    5. 5.5 Summary
  7. Chapter 6 Best Linear Unbiased Prediction
    1. 6.1 Introduction
    2. 6.2 Examples of BLUP
    3. 6.3 Basic Concepts of BLUP
    4. 6.4 Example: Obtaining BLUPs in a Random Effects Model
    5. 6.5 Example: Two-Factor Mixed Model
    6. 6.6 A Multilocation Example
    7. 6.7 Location-Specific Inference in Multicenter Example
    8. 6.8 Summary
  8. 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 Example: One-Way Treatment Structure in a Randomized Complete Block Design Structure—Equal Slopes Model
    4. 7.4 Example: One-Way Treatment Structure in an Incomplete Block Design Structure—Time to Boil Water
    5. 7.5 Example: One-Way Treatment Structure in a Balanced Incomplete Block Design Structure
    6. 7.6 Example: One-Way Treatment Structure in an Unbalanced Incomplete Block Design Structure
    7. 7.7 Example: Split-Plot Design with the Covariate Measured on the Large-Size Experimental Unit or Whole Plot
    8. 7.8 Example: Split-Plot Design with the Covariate Measured on the Small-Size Experimental Unit or Subplot
    9. 7.9 Example: Complex Strip-Plot Design with the Covariate Measured on an Intermediate-Size Experimental Unit
    10. 7.10 Summary
  9. Chapter 8 Random Coefficient Models
    1. 8.1 Introduction
    2. 8.2 Example: One-Way Random Effects Treatment Structure in a Completely Randomized Design Structure
    3. 8.3 Example: Random Student Effects
    4. 8.4 Example: Repeated Measures Growth Study
    5. 8.5 Summary
  10. Chapter 9 Heterogeneous Variance Models
    1. 9.1 Introduction
    2. 9.2 Example: Two-Way Analysis of Variance with Unequal Variances
    3. 9.3 Example: Simple Linear Regression Model with Unequal Variances
    4. 9.4 Example: Nested Model with Unequal Variances for a Random Effect
    5. 9.5 Example: Within-Subject Variability
    6. 9.6 Example: Combining Between- and Within-Subject Heterogeneity
    7. 9.7 Example: Log-Linear Variance Models
    8. 9.8 Summary
  11. Chapter 10 Mixed Model Diagnostics
    1. 10.1 Introduction
    2. 10.2 From Linear to Linear Mixed Models
    3. 10.3 The Influence Diagnostics
    4. 10.4 Example: Unequally Spaced Repeated Measures
    5. 10.5 Summary
  12. Chapter 11 Spatial Variability
    1. 11.1 Introduction
    2. 11.2 Description
    3. 11.3 Spatial Correlation Models
    4. 11.4 Spatial Variability and Mixed Models
    5. 11.5 Example: Estimating Spatial Covariance
    6. 11.6 Using Spatial Covariance for Adjustment: Part 1, Regression
    7. 11.7 Using Spatial Covariance for Adjustment: Part 2, Analysis of Variance
    8. 11.8 Example: Spatial Prediction—Kriging
    9. 11.9 Summary
  13. Chapter 12 Power Calculations for Mixed Models
    1. 12.1 Introduction
    2. 12.2 Power Analysis of a Pilot Study
    3. 12.3 Constructing Power Curves
    4. 12.4 Comparing Spatial Designs
    5. 12.5 Power via Simulation
    6. 12.6 Summary
  14. Chapter 13 Some Bayesian Approaches to Mixed Models
    1. 13.1 Introduction and Background
    2. 13.2 P-Values and Some Alternatives
    3. 13.3 Bayes Factors and Posterior Probabilities of Null Hypotheses
    4. 13.4 Example: Teaching Methods
    5. 13.5 Generating a Sample from the Posterior Distribution with the PRIOR Statement
    6. 13.6 Example: Beetle Fecundity
    7. 13.7 Summary
  15. Chapter 14 Generalized Linear Mixed Models
    1. 14.1 Introduction
    2. 14.2 Two Examples to Illustrate When Generalized Linear Mixed Models Are Needed
    3. 14.3 Generalized Linear Model Background
    4. 14.4 From GLMs to GLMMs
    5. 14.5 Example: Binomial Data in a Multi-center Clinical Trial
    6. 14.6 Example: Count Data in a Split-Plot Design
    7. 14.7 Summary
  16. Chapter 15 Nonlinear Mixed Models
    1. 15.1 Introduction
    2. 15.2 Background on PROC NLMIXED
    3. 15.3 Example: Logistic Growth Curve Model
    4. 15.4 Example: Nested Nonlinear Random Effects Models
    5. 15.5 Example: Zero-Inflated Poisson and Hurdle Poisson Models
    6. 15.6 Example: Joint Survival and Longitudinal Model
    7. 15.7 Example: One-Compartment Pharmacokinetic Model
    8. 15.8 Comparison of PROC NLMIXED and the %NLINMIX Macro
    9. 15.9 Three General Fitting Methods Available in the %NLINMIX Macro
    10. 15.10 Troubleshooting Nonlinear Mixed Model Fitting
    11. 15.11 Summary
  17. Chapter 16 Case Studies
    1. 16.1 Introduction
    2. 16.2 Response Surface Experiment in a Split-Plot Design
    3. 16.3 Response Surface Experiment with Repeated Measures
    4. 16.4 A Split-Plot Experiment with Correlated Whole Plots
    5. 16.5 A Complex Split Plot: Whole Plot Conducted as an Incomplete Latin Square
    6. 16.6 A Complex Strip-Split-Split-Plot Example
    7. 16.7 Unreplicated Split-Plot Design
    8. 16.8 23 Treatment Structure in a Split-Plot Design with the Three-Way Interaction as the Whole-Plot Comparison
    9. 16.9 23 Treatment Structure in an Incomplete Block Design Structure with Balanced Confounding
    10. 16.10 Product Acceptability Study with Crossover and Repeated Measures
    11. 16.11 Random Coefficients Modeling of an AIDS Trial
    12. 16.12 Microarray Example
  18. Appendix 1 Linear Mixed Model Theory
    1. A1.1 Introduction
    2. A1.2 Matrix Notation
    3. A1.3 Formulation of the Mixed Model
    4. A1.4 Estimating Parameters, Predicting Random Effects
    5. A1.5 Statistical Properties
    6. A1.6 Model Selection
    7. A1.7 Inference and Test Statistics
  19. Appendix 2 Data Sets
    1. A2.2 Randomized Block Designs
    2. A2.3 Random Effects Models
    3. A2.4 Analyzing Multi-level and Split-Plot Designs
    4. A2.5 Analysis of Repeated Measures Data
    5. A2.6 Best Linear Unbiased Prediction
    6. A2.7 Analysis of Covariance
    7. A2.8 Random Coefficient Models
    8. A2.9 Heterogeneous Variance Models
    9. A2.10 Mixed Model Diagnostics
    10. A2.11 Spatial Variability
    11. A2.13 Some Bayesian Approaches to Mixed Models
    12. A2.14 Generalized Linear Mixed Models
    13. A2.15 Nonlinear Mixed Models
    14. A2.16 Case Studies
  20. References
  21. Index

Product information

  • Title: SAS for Mixed Models, Second Edition, 2nd Edition
  • Author(s): Ramon C. Littell, George A. Milliken, Walter W. Stroup, Russell D. Wolfinger, Oliver Schabenberger
  • Release date: June 2007
  • Publisher(s): SAS Institute
  • ISBN: 9781599940786