SAS for Mixed Models

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

• ISBN13: 9781590475003
• ISBN10: 1590475003
• Edition: 2nd
• Format: Paperback
• Copyright: 2006-03-30
• Publisher: Sas Inst

Summary

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 this valuable edition of the comprehensive mixed models guide for data analysis, completely revised and updated for SAS?9. 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 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. Includes a free CD-ROM with example SAS code!

Author Biography

Ramon C. Littell Ramon C. Littell, Ph.D., Professor of Statistics at the University of Florida, is the coauthor of several books, including SAS System for Regression, Third Edition, and SAS for Linear Models, Fourth Edition. He has worked with SAS software since 1986. George A. Milliken George A. Milliken, Ph.D., Professor of Statistics at Kansas State University, has been using SAS software since 1974 and has extensive experience with the design and analysis of experiments using mixed models by incorporating the GLM, MIXED, GLIMMIX, and NLMIXED procedures. Walter W. Stroup Walter W. Stroup, Ph.D., Professor and Chair of the Department of Statistics at the University of Nebraska, is the coauthor of SAS for Linear Models, Fourth Edition. He has been using SAS software since 1981. Russell D. Wolfinger Russell D. Wolfinger, Ph.D., is the Director of Scientific Discovery and Genomics at SAS Institute, where he has worked since 1989. Before leading SAS scientific efforts, he authored the MIXED, MULTTEST, KDE, and NLMIXED procedures in SAS/STAT. Oliver Schabenberger Oliver Schabenberger, Ph.D., is a Senior Research Statistician at SAS Institute and has been using SAS software since 1991. He maintains and develops mixed model software and is the author of the GLIMMIX procedure.

Table of Contents

Preface	ix
Introduction	1	(16)
Types of Models That Produce Data	1	(1)
Statistical Models	2	(2)
Fixed and Random Effects	4	(2)
Mixed Models	6	(1)
Typical Studies and the Modeling Issues They Raise	7	(4)
A Typology for Mixed Models	11	(2)
Flowcharts to Select SAS Software to Run Various Mixed Models	13	(4)
Randomized Block Designs	17	(40)
Introduction	18	(1)
Mixed Model for a Randomized Complete Blocks Design	18	(4)
Using Proc mixed to Analyze RCBD Data	22	(20)
Introduction to Theory of Mixed Models	42	(2)
Example of an Unbalanced Two-Way Mixed Model: Incomplete Block Design	44	(12)
Summary	56	(1)
Random Effects Models	57	(36)
Introduction: Descriptions of Random Effects Models	58	(6)
Example: One-Way Random Effects Treatment Structure	64	(11)
Example: A Simple Conditional Hierarchical Linear Model	75	(6)
Example: Three-Level Nested Design Structure	81	(7)
Example: A Two-Way Random Effects Treatment Structure to Estimate Heritability	88	(3)
Summary	91	(2)
Multi-factor Treatment Designs with Multiple Error Terms	93	(66)
Introduction	94	(1)
Treatment and Experiment Structure and Associated Models	94	(8)
Inference with Mixed Models for Factorial Treatment Designs	102	(11)
Example: A Split-Plot Semiconductor Experiment	113	(17)
Comparison with Proc GLM	130	(5)
Example: Type x Dose Response	135	(13)
Example: Variance Component Estimates Equal to Zero	148	(6)
More on Proc GLM Compared to Proc Mixed: Incomplete Blocks, Missing Data, and Estimability	154	(2)
Summary	156	(3)
Analysis of Repeated Measures Data	159	(46)
Introduction	160	(3)
Example: Mixed Model Analysis of Data from Basic Repeated Measures Design	163	(11)
Modeling Covariance Structure	174	(24)
Example: Unequally Spaced Repeated Measures	198	(4)
Summary	202	(3)
Best Linear Unbiased Prediction	205	(38)
Introduction	206	(1)
Examples of BLUP	206	(4)
Basic Concepts of BLUP	210	(2)
Example: Obtaining BLUPs in a Random Effects Model	212	(7)
Example: Two-Factor Mixed Model	219	(7)
A Multilocation Example	226	(8)
Location-Specific Inference in Multicenter Example	234	(7)
Summary	241	(2)
Analysis of Covariance	243	(74)
Introduction	244	(1)
One-Way Fixed Effects Treatment Structure with Simple Linear Regression Models	245	(6)
Example: One-Way Treatment Structure in a Randomized Complete Block Design Structure---Equal Slopes Model	251	(12)
Example: One-Way Treatment Structure in an Incomplete Block Design Structure---Time to Boil Water	263	(9)
Example: One-Way Treatment Structure in a Balanced Incomplete Block Design Structure	272	(9)
Example: One-Way Treatment Structure in an Unbalanced Incomplete Block Design Structure	281	(5)
Example: Split-Plot Design with the Covariate Measured on the Large-Size Experimental Unit or Whole Plot	286	(11)
Example: Split-Plot Design with the Covariate Measured on the Small-Size Experimental Unit or Subplot	297	(11)
Example: Complex Strip-Plot Design with the Covariate Measured on an Intermediate-Size Experimental Unit	308	(7)
Summary	315	(2)
Random Coefficient Models	317	(26)
Introduction	317	(3)
Example: One-Way Random Effects Treatment Structure in a Completely Randomized Design Structure	320	(6)
Example: Random Student Effects	326	(4)
Example: Repeated Measures Growth Study	330	(11)
Summary	341	(2)
Heterogeneous Variance Models	343	(70)
Introduction	344	(1)
Example: Two-Way Analysis of Variance with Unequal Variances	345	(9)
Example: Simple Linear Regression Model with Unequal Variances	354	(12)
Example: Nested Model with Unequal Variances for a Random Effect	366	(8)
Example: Within-Subject Variability	374	(19)
Example: Combining Between- and Within-Subject Heterogeneity	393	(9)
Example: Log-Linear Variance Models	402	(9)
Summary	411	(2)
Mixed Model Diagnostics	413	(24)
Introduction	413	(2)
From Linear to Linear Mixed Models	415	(9)
The Influence Diagnostics	424	(2)
Example: Unequally Spaced Repeated Measures	426	(9)
Summary	435	(2)
Spatial Variability	437	(42)
Introduction	438	(1)
Description	438	(2)
Spatial Correlation Models	440	(2)
Spatial Variability and Mixed Models	442	(5)
Example: Estimating Spatial Covariance	447	(10)
Using Spatial Covariance for Adjustment: Part 1, Regression	457	(3)
Using Spatial Covariance for Adjustment: Part 2, Analysis of Variance	460	(11)
Example: Spatial Prediction---Kriging	471	(7)
Summary	478	(1)
Power Calculations for Mixed Models	479	(18)
Introduction	479	(1)
Power Analysis of a Pilot Study	480	(3)
Constructing Power Curves	483	(3)
Comparing Spatial Designs	486	(3)
Power via Simulation	489	(6)
Summary	495	(2)
Some Bayesian Approaches to Mixed Models	497	(28)
Introduction and Background	497	(2)
P-Values and Some Alternatives	499	(3)
Bayes Factors and Posterior Probabilities of Null Hypotheses	502	(5)
Example: Teaching Methods	507	(2)
Generating a Sample from the Posterior Distribution with the Prior Statement	509	(2)
Example: Beetle Fecundity	511	(13)
Summary	524	(1)
Generalized Linear Mixed Models	525	(42)
Introduction	526	(1)
Two Examples to Illustrate When Generalized Linear Mixed Models Are Needed	527	(2)
Generalized Linear Model Background	529	(9)
From GLMs to GLMMs	538	(4)
Example: Binomial Data in a Multi-center Clinical Trial	542	(15)
Example: Count Data in a Split-Plot Design	557	(9)
Summary	566	(1)
Nonlinear Mixed Models	567	(70)
Introduction	568	(1)
Background on Proc Nlmixed	569	(2)
Example: Logistic Growth Curve Model	571	(16)
Example: Nested Nonlinear Random Effects Models	587	(2)
Example: Zero-Inflated Poisson and Hurdle Poisson Models	589	(6)
Example: Joint Survival and Longitudinal Model	595	(12)
Example: One-Compartment Pharmacokinetic Model	607	(16)
Comparison of Proc Nlmixed and the %Nlinmix Macro	623	(2)
Three General Fitting Methods Available in the %Nlinmix Macro	625	(4)
Troubleshooting Nonlinear Mixed Model Fitting	629	(5)
Summary	634	(3)
Case Studies	637	(96)
Introduction	638	(1)
Response Surface Experiment in a Split-Plot Design	639	(4)
Response Surface Experiment with Repeated Measures	643	(7)
A Split-Plot Experiment with Correlated Whole Plots	650	(9)
A Complex Split Plot: Whole Plot Conducted as an Incomplete Latin Square	659	(8)
A Complex Strip-Split-Split-Plot Example	667	(7)
Unreplicated Split-Plot Design	674	(10)
23 Treatment Structure in a Split-Plot Design with the Three-Way Interaction as the Whole-Plot Comparison	684	(10)
23 Treatment Structure in an Incomplete Block Design Structure with Balanced Confounding	694	(5)
Product Acceptability Study with Crossover and Repeated Measures	699	(17)
Random Coefficients Modeling of an AIDS Trial	716	(11)
Microarray Example	727	(6)
Appendix 1 Linear Mixed Model Theory	733	(24)
Introduction	734	(1)
Matrix Notation	734	(1)
Formulation of the Mixed Model	735	(7)
Estimating Parameters, Predicting Random Effects	742	(9)
Statistical Properties	751	(1)
Model Selection	752	(2)
Inference and Test Statistics	754	(3)
Appendix 2 Data Sets	757	(24)
Randomized Block Designs	759	(1)
Random Effects Models	759	(2)
Analyzing Multi-level and Split-Plot Designs	761	(1)
Analysis of Repeated Measures Data	762	(2)
Best Linear Unbiased Prediction	764	(1)
Analysis of Covariance	765	(3)
Random Coefficient Models	768	(1)
Heterogeneous Variance Models	769	(2)
Mixed Model Diagnostics	771	(1)
Spatial Variability	772	(1)
Some Bayesian Approaches to Mixed Models	773	(1)
Generalized Linear Mixed Models	774	(1)
Nonlinear Mixed Models	775	(1)
Case Studies	776	(5)
References	781	(14)
Index	795