SAS System for Mixed Models

Chapter 1 A Setting for Mixed Models Applications: Randomized Blocks Designs

1.1 Introduction
1.2 Mixed Model for a Randomized Complete Blocks Design
1.3 Using PROC MIXED to Analyze RCBD Data
1.4 Introduction to the Theory of Linear Models
1.5 Example of an Unbalanced Two-way Mixed Model: Incomplete Block Design
1.6 Summary
1.7 References

Chapter 2 Common Mixed Models

2.1 Introduction
2.2 Examples: Split-Plot Experiments
2.3 Using PROC MIXED to Analyze a Balanced Split-Plot Experiment
2.4 Comparison with the Analysis of a Split-Plot Experiment Using PROC GLM
2.5 Split-Plot Experiments with Whole Plots in Randomized Blocks
2.6 Standard Errors and Implied Inference Space
2.7 Unbalanced Split-Plot Experiments
2.8 Multilocation Trial
2.9 Summary
2.10 References

Chapter 3 Analysis of Repeated Measures Data

3.1 Introduction
3.2 Example: Mixed Model Analysis of Data from Basic Repeated Measures Design
3.3 Comparison of PROC MIXED and PROC GLM for Analysis of Repeated Measures Data
3.4 Missing Data in Repeated Measures
3.5 Example: Unequally Spaced Repeated Measures
3.6 Example: Doubly Repeated Measures
3.7 Summary
3.8 References

Chapter 4 Random Effects Models

4.1 Introduction: Descriptions of Random-Effects Models
4.2 Example: One-way Random-Effects Treatment Structure
4.3 Example: A Simple Conditional Hierarchical Linear Model
4.4 Example: Three Level Nested Design Structure
4.5 Example: A Two-way Random Effects Treatment Structure to Estimate Heritability
4.6 Summary
4.7 References

Chapter 5 Analysis of Covariance

5.1 Introduction
5.2 One-way Fixed-Effects Treatment Structure with Simple Linear Regression Models
5.3 Example: One-way Treatment Structure in a Randomized Complete Block Design Structure
5.4 Example: One-way Treatment Structure in a Balanced Incomplete Block Design Structure
5.5 Example: One-way Treatment Structure in an Unbalanced Incomplete Block Design Structure
5.6 Example: Split-Plot Design with the Covariate Measured on the Large Size Experimental Unit or Whole Plot
5.7 Example: Split-Plot Design with the Covariate Measured on the Small Size Experimental Unit or Subplot
5.8 Example: Complex Strip-Plot Design with the Covariate Measured on an Intermediate Size Experimental Unit
5.9 Summary
5.10 References

Chapter 6 Best Linear Unbiased Prediction

6.1 Introduction
6.2 Examples of BLUP
6.3 Basic Concepts for BLUP
6.4 Example: Obtaining BLUPs in a Random-Effects Model
6.5 Example: Two-Factor Mixed Model
6.6 A Multilocation Example
6.7 Summary
6.8 References

Chapter 7 Random Coefficient Models

7.1 Introduction
7.2 Examples
7.3 Summary
7.4 References

Chapter 8 Heterogeneous Variance Models

8.1 Introduction
8.2 Example: Within-Subject Heterogeneity
8.3 Example: Combining Between- and Within-Subject Heterogeneity
8.4 Example: Log-Linear Variance Models
8.5 Summary
8.6 References

Chapter 9 Spatial Variability

9.1 Introduction
9.2 Description
9.3 Spatial Correlation Models
9.4 Spatial Variability and Mixed Models
9.5 Example: Estimating Spatial Covariance
9.6 Examples: Using Spatial Covariance for Adjustment
9.7 A Caution about Estimating Spatial Covariance
9.8 Summary
9.9 References

Chapter 10 Case Studies

10.1 Introduction
10.2 Response Surface Experiment in a Split-Plot Design
10.3 A Split-Plot Experiment with Correlated Whole Plots
10.4 A Complex Split Plot: Whole Plot Conducted As an Incomplete Latin Square
10.5 A Complex Strip-Split-Split-Plot Example
10.6 Treatment Structure in a Split-Plot Design with the Three-way Interaction As the Whole-Plot Comparison
10.7 Treatment Structure in an Incomplete Block Design Structure with Balanced Confounding
10.8 Product Acceptability Study with Cross-over and Repeated Measures
10.9 An On-Farm Trial
10.10 Random Coefficients Modeling of an AIDS Trial
10.11 References

Chapter 11 Generalized Linear Mixed Models

11.1 Introduction
11.2 Two Examples to Illustrate When Generalized Linear Mixed Models Are Needed
11.3 Generalized Linear Model Background
11.4 Incorporating Random Effects into Generalized Linear Models
11.5 Example: Mixed Model with Binomial Errors
11.6 Example: A Mixed Model with Count Data
11.7 Summary
11.8 References

Chapter 12 Nonlinear Mixed Models

12.1 Introduction
12.2 Three General Methods Available in the NLINMIX Macro
12.3 Theoretical Details for the Three Methods
12.4 Example: Logistic Growth Curve
12.5 Example: One-Compartment Pharmacokinetic Model
12.6 Problems with the NLINMIX Macro?
12.7 Summary
12.8 References

Appendix 1 Mixed Models Theory
Introduction
Matrix Notation
Formulation of the Mixed Model
Example: Growth Curve with Compound Symmetry
Example: Split-Plot Design
Estimating G and R in the Mixed Model
Estimating and u in the Mixed Model
Model Selection
Statistical Properties
Inference and Test Statistics
References
Appendix 2 GLIMMIX Macro
Appendix 3 NLINMIX Macro
Appendix 4 SAS Datasets
Data Set 1.2.4 BOND
Data Set 1.5.1 PBIB
Data Set 2.2(a) Data from Cultivar-Inoculation Trial
Data Set 2.2(b) Data from Semiconductor Example
Data Set 2.8.1 Multilocation Trial
Data Set 3.2(a) WEIGHTS
Data Set 3.2(b) WEIGHT2
Data Set 3.2(c) AVG
Data Set 3.4(a) WTSMISS
Data Set 3.4(b) WT2MISS
Data Set 3.5 HR
Data Set 3.6 DEMAND
Data Set 4.2 Mississippi River
Data Set 4.4 Semiconductor
Data Set 4.5 Genetics
Data Set 5.3 Average Daily Gain
Data Set 5.4 Balanced Incomplete Block
Data Set 5.5 Unbalanced Incomplete Block
Data Set 5.6 Teaching Methods I
Data Set 5.7 Teaching Methods II
Data Set 5.8 Wafer Types
Data Set 6.4 Animal Breeding
Data Set 6.5 Machine Operator
Data Set 7.2 Winter Wheat
Data Set 8.2 DIAL
Data Set 8.3 GRIP
Data Set 8.4.1 PREETCH
Data Set 9.5 Agronomic Uniformity Trial
Data Set 9.6.1 Water Drainage Characteristics
Data Set 9.6.2 Wheat Yield
Data Set 10.2.1 DESIGN
Data Set 10.3.1 Response of Maize to Irrigation
Data Set 10.4.1 Complex Split-Plot
Data Set 10.5.1 Methods of Rangeland Reclamation
Data Set 10.6.1 FAC-SP
Data Set 10.7.1 Photo Resist Coating Experiment
Data Set 10.8.1 Product Acceptability Study
Data Set 10.9.1 On-Farm Trial
Data Set 10.10 CD
Data Set 11.5 NEW
Data Set 11.6 A
Data Set 12.4 Tree
Data Set 12.5 PHENO
Index

SAS System for Mixed Models

Contents