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Tables of Contents for Mixed-Effects Models in s and S-Plus
Chapter/Section Title
Page #
Page Count
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