book

SAS for Mixed Models, Second Edition, 2nd Edition

by Ramon C. Littell, George A. Milliken, Walter W. Stroup, Russell D. Wolfinger, Oliver Schabenberger

June 2007

Intermediate to advanced

828 pages

22h 20m

English

SAS Institute

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Preface
Chapter 1 Introduction
1.1 Types of Models That Produce Data1.2 Statistical Models1.3 Fixed and Random Effects1.4 Mixed Models1.5 Typical Studies and the Modeling Issues They Raise1.6 A Typology for Mixed Models1.7 Flowcharts to Select SAS Software to Run Various Mixed Models
Chapter 2 Randomized Block Designs
2.1 Introduction2.2 Mixed Model for a Randomized Complete Blocks Design2.3 Using PROC MIXED to Analyze RCBD Data2.4 Introduction to Theory of Mixed Models2.5 Example of an Unbalanced Two-Way Mixed Model: Incomplete Block Design2.6 Summary
Chapter 3 Random Effects Models
3.1 Introduction: Descriptions of Random Effects Models3.2 Example: One-Way Random Effects Treatment Structure3.3 Example: A Simple Conditional Hierarchical Linear Model3.4 Example: Three-Level Nested Design Structure3.5 Example: A Two-Way Random Effects Treatment Structure to Estimate Heritability3.6 Summary
Chapter 4 Multi-factor Treatment Designs with Multiple Error Terms
4.1 Introduction4.2 Treatment and Experiment Structure and Associated Models4.3 Inference with Mixed Models for Factorial Treatment Designs4.4 Example: A Split-Plot Semiconductor Experiment4.5 Comparison with PROC GLM
4.6 Example: Type × Dose Response
4.7 Example: Variance Component Estimates Equal to Zero4.8 More on PROC GLM Compared to PROC MIXED: Incomplete Blocks, Missing Data, and Estimability4.9 Summary
Chapter 5 Analysis of Repeated Measures Data
5.1 Introduction5.2 Example: Mixed Model Analysis of Data from Basic Repeated Measures Design5.3 Modeling Covariance Structure5.4 Example: Unequally Spaced Repeated Measures5.5 Summary
Chapter 6 Best Linear Unbiased Prediction
6.1 Introduction6.2 Examples of BLUP6.3 Basic Concepts of BLUP6.4 Example: Obtaining BLUPs in a Random Effects Model6.5 Example: Two-Factor Mixed Model6.6 A Multilocation Example6.7 Location-Specific Inference in Multicenter Example6.8 Summary
Chapter 7 Analysis of Covariance
7.1 Introduction7.2 One-Way Fixed Effects Treatment Structure with Simple Linear Regression Models7.3 Example: One-Way Treatment Structure in a Randomized Complete Block Design Structure—Equal Slopes Model7.4 Example: One-Way Treatment Structure in an Incomplete Block Design Structure—Time to Boil Water7.5 Example: One-Way Treatment Structure in a Balanced Incomplete Block Design Structure7.6 Example: One-Way Treatment Structure in an Unbalanced Incomplete Block Design Structure
7.7 Example: Split-Plot Design with the Covariate Measured on the Large-Size Experimental Unit or Whole Plot
7.8 Example: Split-Plot Design with the Covariate Measured on the Small-Size Experimental Unit or Subplot7.9 Example: Complex Strip-Plot Design with the Covariate Measured on an Intermediate-Size Experimental Unit7.10 Summary

Chapter 8 Random Coefficient Models
8.1 Introduction8.2 Example: One-Way Random Effects Treatment Structure in a Completely Randomized Design Structure8.3 Example: Random Student Effects8.4 Example: Repeated Measures Growth Study8.5 Summary
Chapter 9 Heterogeneous Variance Models
9.1 Introduction9.2 Example: Two-Way Analysis of Variance with Unequal Variances9.3 Example: Simple Linear Regression Model with Unequal Variances9.4 Example: Nested Model with Unequal Variances for a Random Effect9.5 Example: Within-Subject Variability9.6 Example: Combining Between- and Within-Subject Heterogeneity
9.7 Example: Log-Linear Variance Models
9.8 Summary
Chapter 10 Mixed Model Diagnostics
10.1 Introduction10.2 From Linear to Linear Mixed Models10.3 The Influence Diagnostics10.4 Example: Unequally Spaced Repeated Measures10.5 Summary
Chapter 11 Spatial Variability
11.1 Introduction11.2 Description11.3 Spatial Correlation Models11.4 Spatial Variability and Mixed Models11.5 Example: Estimating Spatial Covariance11.6 Using Spatial Covariance for Adjustment: Part 1, Regression11.7 Using Spatial Covariance for Adjustment: Part 2, Analysis of Variance11.8 Example: Spatial Prediction—Kriging11.9 Summary
Chapter 12 Power Calculations for Mixed Models
12.1 Introduction12.2 Power Analysis of a Pilot Study12.3 Constructing Power Curves12.4 Comparing Spatial Designs12.5 Power via Simulation12.6 Summary
Chapter 13 Some Bayesian Approaches to Mixed Models
13.1 Introduction and Background13.2 P-Values and Some Alternatives13.3 Bayes Factors and Posterior Probabilities of Null Hypotheses13.4 Example: Teaching Methods13.5 Generating a Sample from the Posterior Distribution with the PRIOR Statement13.6 Example: Beetle Fecundity13.7 Summary
Chapter 14 Generalized Linear Mixed Models
14.1 Introduction14.2 Two Examples to Illustrate When Generalized Linear Mixed Models Are Needed14.3 Generalized Linear Model Background14.4 From GLMs to GLMMs14.5 Example: Binomial Data in a Multi-center Clinical Trial14.6 Example: Count Data in a Split-Plot Design14.7 Summary
Chapter 15 Nonlinear Mixed Models
15.1 Introduction15.2 Background on PROC NLMIXED15.3 Example: Logistic Growth Curve Model15.4 Example: Nested Nonlinear Random Effects Models15.5 Example: Zero-Inflated Poisson and Hurdle Poisson Models15.6 Example: Joint Survival and Longitudinal Model
15.7 Example: One-Compartment Pharmacokinetic Model
15.8 Comparison of PROC NLMIXED and the %NLINMIX Macro15.9 Three General Fitting Methods Available in the %NLINMIX Macro15.10 Troubleshooting Nonlinear Mixed Model Fitting15.11 Summary
Chapter 16 Case Studies
16.1 Introduction16.2 Response Surface Experiment in a Split-Plot Design16.3 Response Surface Experiment with Repeated Measures16.4 A Split-Plot Experiment with Correlated Whole Plots16.5 A Complex Split Plot: Whole Plot Conducted as an Incomplete Latin Square16.6 A Complex Strip-Split-Split-Plot Example16.7 Unreplicated Split-Plot Design
16.8 23 Treatment Structure in a Split-Plot Design with the Three-Way Interaction as the Whole-Plot Comparison
16.9 23 Treatment Structure in an Incomplete Block Design Structure with Balanced Confounding16.10 Product Acceptability Study with Crossover and Repeated Measures16.11 Random Coefficients Modeling of an AIDS Trial16.12 Microarray Example
Appendix 1 Linear Mixed Model Theory
A1.1 IntroductionA1.2 Matrix NotationA1.3 Formulation of the Mixed ModelA1.4 Estimating Parameters, Predicting Random EffectsA1.5 Statistical PropertiesA1.6 Model SelectionA1.7 Inference and Test Statistics
Appendix 2 Data Sets
A2.2 Randomized Block DesignsA2.3 Random Effects ModelsA2.4 Analyzing Multi-level and Split-Plot DesignsA2.5 Analysis of Repeated Measures DataA2.6 Best Linear Unbiased PredictionA2.7 Analysis of CovarianceA2.8 Random Coefficient ModelsA2.9 Heterogeneous Variance ModelsA2.10 Mixed Model DiagnosticsA2.11 Spatial VariabilityA2.13 Some Bayesian Approaches to Mixed ModelsA2.14 Generalized Linear Mixed ModelsA2.15 Nonlinear Mixed ModelsA2.16 Case Studies
References
Index

Overview

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.

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