Mixed-Effects Models in s and S-Plus

by Pinheiro, Jose C.; Bates, Douglas M.

• ISBN13: 9780387989570
• ISBN10: 0387989579
• Format: Hardcover
• Copyright: 2000-05-01
• Publisher: Springer Nature

Summary

This book provides an overview of the theory and application of linear and nonlinear mixed-effects models in the analysis of grouped data, such as longitudinal data, repeated measures, and multilevel data. Over 170 figures are included in the book.

Author Biography

Douglas M. Bates is Professor of Statistics at the University of Wisconsin-Madison.

Table of Contents

Preface	vii
I Linear Mixed-Effects Models	1	(270)
Linear Mixed-Effects Models	3	(54)
A Simple Example of Random Effects	4	(8)
Fitting the Random-Effects Model With 1me	8	(3)
Assessing the Fitted Model	11	(1)
A Randomized Block Design	12	(9)
Choosing Contrasts for Fixed-Effects Terms	14	(5)
Examining the Model	19	(2)
Mixed-Effects Models for Replicated, Blocked Designs	21	(9)
Fitting Random Interaction Terms	23	(2)
Unbalanced Data	25	(2)
More General Models for the Random Interaction Effects	27	(3)
An Analysis of Covariance Model	30	(10)
Modeling Simple Linear Growth Curves	30	(7)
Predictions of the Response and the Random Effects	37	(3)
Models for Nested Classification Factors	40	(5)
Model Building for Multilevel Models	44	(1)
A Spit-Plot Experiment	45	(7)
Chapter Summary	52	(5)
Exercises	52	(5)
Theory and Computational Methods for LME Models	57	(40)
The LME Model Formulation	58	(4)
Single Level of Grouping	58	(2)
A Multilevel LME Model	60	(2)
Likelihood Estimation for LME Models	62	(19)
The Single-Level LME Likelihood Function	62	(4)
Orthogonal-Triangular Decompositions	66	(2)
Evaluating the Likelihood Through Decompositions	68	(3)
Components of the Profiled Log-Likelihood	71	(4)
Restricted Likelihood Estimation	75	(2)
Multiple Levels of Random Effects	77	(1)
Parameterizing Relative Precision Factors	78	(1)
Optimization Algorithms	79	(2)
Approximate Distributions	81	(1)
Hypothesis Tests and Confidence Intervals	82	(12)
Likelihood Ratio Tests	83	(4)
Hypothesis Tests for Fixed-Effects Terms	87	(5)
Confidence Intervals	92	(2)
Fitted Values and Predictions	94	(1)
Chapter Summary	94	(3)
Exercises	96	(1)
Describing the Structure of Grouped Data	97	(36)
The Display Formula and Its Components	97	(4)
Constructing groupedData Objects	101	(9)
Roles of Other Experimental or Blocking Factors	104	(4)
Constructors for Balanced Data	108	(2)
Controlling Trellis Graphics Presentations of Grouped Data	110	(10)
Layout of the Trellis Plot	110	(3)
Modifying the Vertical and Horizontal Scales	113	(1)
Modifying the Panel Function	114	(2)
Plots of Multiply-Nested Data	116	(4)
Summaries	120	(10)
Chapter Summary	130	(3)
Exercises	130	(3)
Fitting Linear Mixed-Effects Models	133	(68)
Fitting Linear Models in S with 1m and 1mList	134	(12)
The 1mList Function	139	(7)
Fitting Linear Mixed-Effects Models with 1me	146	(28)
Fitting Single-Level Models	146	(11)
Patterned Variance--Covariance Matrices for the Random Effects: The pdMat Classes	157	(10)
Fitting Multilevel Models	167	(7)
Examining a Fitted Model	174	(22)
Assessing Assumptions on the Within-Group Error	174	(13)
Assessing Assumptions on the Random Effects	187	(9)
Chapter Summary	196	(5)
Exercises	197	(4)
Extending the Basic Linear Mixed-Effects Model	201	(70)
General Formulation of the Extended Model	202	(4)
Estimation and Computational Methods	202	(1)
The GLS model	203	(2)
Decomposing the Within-Group Variance--Covariance Structure	205	(1)
Variance Functions for Modeling Heteroscedasticity	206	(20)
varFunc classes in nlme	208	(6)
Using varFunc classes with lme	214	(12)
Correlation Structures for Modeling Dependence	226	(23)
Serial Correlation Structures	226	(4)
Spatial Correlation Structures	230	(2)
corStruct classes in nlme	232	(7)
Using corStruct Classes with lme	239	(10)
Fitting Extended Linear Models with gls	249	(17)
Chapter Summary	266	(5)
Exercises	267	(4)
II Nonlinear Mixed-Effects Models	271	(144)
NLME Models: Basic Concepts and Motivating Examples	273	(32)
LME Models vs. NLME Models	273	(4)
Indomethicin Kinetics	277	(10)
Growth of Soybean Plants	287	(7)
Clinical Study of Phenobarbital Kinetics	294	(6)
Chapter Summary	300	(5)
Exercises	301	(4)
Theory and Computational Methods for NLME Models	305	(32)
The NLME Model Formulation	306	(6)
Single-Level of Grouping	306	(3)
Multilevel NLME Models	309	(1)
Other NLME Models	310	(2)
Estimation and Inference in NLME Models	312	(12)
Likelihood Estimation	312	(10)
Inference and Predictions	322	(2)
Computational Methods	324	(4)
Extending the Basic NLME Model	328	(4)
General model formulation	328	(1)
Estimation and Computational Methods	329	(3)
An Extended Nonlinear Regression Model	332	(4)
General Model Formulation	333	(1)
Estimation and Computational Methods	334	(2)
Chapter Summary	336	(1)
Fitting Nonlinear Mixed-Effects Models	337	(78)
Fitting Nonlinear Models in S with nls and nlsList	338	(16)
Using the nls Function	338	(4)
Self-Starting Nonlinear Model Functions	342	(5)
Separate Nonlinear Fits by Group: The nlsList Function	347	(7)
Fitting Nonlinear Mixed-Effects Models with nlme	354	(37)
Fitting Single-Level nlme Models	354	(11)
Using Covariates with nlme	365	(20)
Fitting Multilevel nlme Models	385	(6)
Extending the Basic nlme Model	391	(18)
Variance Functions in nlme	391	(4)
Correlation Structures in nlme	395	(6)
Fitting Extended Nonlinear Regression Models with gnls	401	(8)
Chapter Summary	409	(6)
Exercises	410	(5)
References	415	(8)
A Data Used in Examples and Exercises	423	(28)
A.1 Alfalfa---Split-Plot Experiment on Varieties of Alfalfa	425	(1)
A.2 Assay---Bioassay on Cell Culture Plate	425	(2)
A.3 BodyWeight---Body Weight Growth in Rats	427	(1)
A.4 Cefamandole---Pharmacokinetics of Cefamandole	427	(1)
A.5 CO2---Carbon Dioxide Uptake	428	(1)
A.6 Dialyzer---High-Flux Hemodialyzer	429	(1)
A.7 DNase---Assay Data for the Protein DNase	429	(1)
A.8 Earthquake---Earthquake Intensity	430	(1)
A.9 ergoStool---Ergometrics Experiment with Stool Types	431	(1)
A.10 Glucose2---Glucose Levels Following Alcohol Ingestion	432	(1)
A.11 IGF---Radioimmunoassay of IGF-I Protein	433	(1)
A.12 Indometh---Indomethicin Kinetics	433	(1)
A.13 Loblolly---Growth of Loblolly Pine Trees	434	(1)
A.14 Machines---Productivity Scores for Machines and Workers	435	(1)
A.15 Oats---Split-plot Experiment on Varieties of Oats	435	(1)
A.16 Orange---Growth of Orange Trees	436	(1)
A.17 Orthodont---Orthodontic Growth Data	436	(1)
A.18 Ovary---Counts of Ovarian Follicles	437	(1)
A.19 Oxboys---Heights of Boys in Oxford	437	(1)
A.20 Oxide---Variability in Semiconductor Manufacturing	437	(1)
A.21 PBG---Effect of Phenylbiguanide on Blood Pressure	438	(1)
A.22 PBIB---A Partially Balanced Incomplete Block Design	439	(1)
A.23 Phenobarb---Phenobarbitol Kinetics	440	(1)
A.24 Pixel---Pixel Intensity in Lymphnodes	440	(1)
A.25 Quinidine---Quinidine Kinetics	441	(2)
A.26 Rail---Evaluation of Stress in Rails	443	(1)
A.27 Soybean---Soybean Leaf Weight over Time	443	(1)
A.28 Spruce---Growth of Spruce Trees	444	(1)
A.29 Theoph---Theophylline Kinetics	444	(4)
A.30 Wafer---Modeling of Analog MOS Circuits	448	(1)
A.31 Wheat2---Wheat Yield Trials	448	(3)
B S Functions and Classes	451	(72)
ACF	451	(1)
ACF.lme	452	(1)
anova.lme	453	(2)
coef.lme	455	(2)
coef.lmList	457	(1)
fitted.lme	458	(1)
fixef	459	(1)
gapply	460	(1)
getGroups	461	(1)
gls	462	(2)
gnls	464	(2)
groupedData	466	(3)
gsummary	469	(2)
intervals	471	(1)
intervals.lme	471	(2)
intervals.lmList	473	(1)
lme	474	(2)
lmeControl	476	(2)
lmList	478	(1)
logLik	479	(1)
nlme	479	(4)
nlmeControl	483	(2)
nlsList	485	(1)
pairs.lme	486	(2)
plot.lme	488	(2)
plot.nfnGroupedData	490	(2)
plot.nmGroupedData	492	(2)
plot.Variogram	494	(1)
predict.lme	495	(2)
qqnorm.lme	497	(1)
ranef	498	(1)
ranef.lme	499	(2)
ranef.lmList	501	(2)
residuals.lme	503	(1)
selfStart	504	(1)
selfStart.default	505	(1)
selfStart.formula	506	(1)
Variogram	507	(1)
Variogram.lme	508	(3)
C A Collection of Self-Starting Nonlinear Regression Models
C.1 SSasymp---The Asymptotic Regression Model	511	(1)
C.1.1 Starting Estimates for SSasymp	511	(1)
C.2 SSasympOff---Asymptotic Regression with an Offset	512	(1)
C.2.1 Starting Estimates for SSasympOff	512	(1)
C.3 SSasympOrig---Asymptotic Regression Through the Origin	513	(1)
C.3.1 Starting Estimates for SSasympOrig	513	(1)
C.4 SSbiexp---Biexponential Model	514	(2)
C.4.1 Starting Estimates for SSbiexp	515	(1)
C.5 SSfol---First-Order Compartment Model	516	(1)
C.5.1 Starting Estimates for SSfol	516	(1)
C.6 SSfpl---Four-Parameter Logistic Model	517	(2)
C.6.1 Starting Estimates for SSfpl	518	(1)
C.7 SSlogis---Simple Logistic Model	519	(1)
C.7.1 Starting Estimates for SSlogis	519	(1)
C.8 SSmicmen---Michaelis-Menten Model	520	(3)
C.8.1 Starting Estimates for SSmicmen	521	(2)
Index	523