Mixed-effects models in S and S-PLUS:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York, NY
Springer
2000
|
| Series: | Statistics and computing
|
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | XVIII, 528 S. graph. Darst. |
| ISBN: | 9781441903174 |
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MARC
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| 100 | 1 | |a Pinheiro, José C. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Mixed-effects models in S and S-PLUS |c José Pinheiro ; Douglas Bates |
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| 300 | |a XVIII, 528 S. |b graph. Darst. | ||
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Contents
Preface
vii
I Linear Mixed-Effects Models
1
1
Linear Mixed-Effects Models
3
1.1
A Simple Example of Random Effects
. 4
1.1.1
Fitting the Random-Effects Model With
Ime
. 8
1.1.2
Assessing the Fitted Model
. 11
1.2
A Randomized Block Design
. 12
1.2.1
Choosing Contrasts for Fixed-Effects Terms
. 14
1.2.2
Examining the Model
. 19
1.3
Mixed-Effects Models for Replicated, Blocked Designs
. 21
1.3.1
Fitting Random Interaction Terms
. 23
1.3.2
Unbalanced Data
. 25
1.3.3
More General Models for the Random Interaction
Effects
. 27
1.4
An Analysis of Covariance Model
. 30
1.4.1
Modeling Simple Linear Growth Curves
. 30
1.4.2
Predictions of the Response and the Random Effects
37
1.5
Models for Nested Classification Factors
. 40
1.5.1
Model Building for Multilevel Models
. 44
1.6
A Split-Plot Experiment
. 45
1.7
Chapter Summary
. 52
Exercises
. 52
Contents
Theory and Computational Methods for LME Models
57
2.1
The LME Model Formulation
. 58
2.1.1
Single Level of Grouping
. 58
2.1.2
A Multilevel LME Model
. 60
2.2
Likelihood Estimation for LME Models
. 62
2.2.1
The Single-Level LME Likelihood Function
. 62
2.2.2
Orthogonal-Triangular Decompositions
. 66
2.2.3
Evaluating the Likelihood Through Decompositions
68
2.2.4
Components of the Profiled Log-Likelihood
. 71
2.2.5
Restricted Likelihood Estimation
. 75
2.2.6
Multiple Levels of Random Effects
. 77
2.2.7
Parameterizing Relative Precision Factors
. 78
2.2.8
Optimization Algorithms
. 79
2.3
Approximate Distributions
. 81
2.4
Hypothesis Tests and Confidence Intervals
. 82
2.4.1
Likelihood Ratio Tests
. 83
2.4.2
Hypothesis Tests for Fixed-Effects Terms
. 87
2.4.3
Confidence Intervals
. 92
2.5
Fitted Values and Predictions
. 94
2.6
Chapter Summary
. 94
Exercises
. 96
Describing the Structure of Grouped Data
97
3.1
The Display Formula and Its Components
. 97
3.2
Constructing groupedData Objects
. 101
3.2.1
Roles of Other Experimental or Blocking Factors
. . 104
3.2.2
Constructors for Balanced Data
. 108
3.3
Controlling Trellis Graphics Presentations of Grouped Data
110
3.3.1
Layout of the Trellis Plot
. 110
3.3.2
Modifying the Vertical and Horizontal Scales
. 113
3.3.3
Modifying the Panel Function
. 114
3.3.4
Plots of Multiply-Nested Data
. 116
3.4
Summaries
. 120
3.5
Chapter Summary
. 130
Exercises
. 130
Fitting Linear Mixed-Effects Models
133
4.1
Fitting Linear Models in
S
with lm and lmList
. 134
4.1.1
The lmList Function
. 139
4.2
Fitting Linear Mixed-Effects Models with
Ime
. 146
4.2.1
Fitting Single-Level Models
. 146
4.2.2
Patterned Variance-Covariance Matrices for the
Random Effects: The pdMat Classes
. 157
4.2.3
Fitting Multilevel Models
. 167
4.3
Examining a Fitted Model
. 174
Contents xiii
4.3.1
Assessing Assumptions on the Within-Group Error
. 174
4.3.2
Assessing Assumptions on the Random Effects
. . . 187
4.4
Chapter Summary
. 196
Exercises
. 197
Extending the Basic Linear Mixed-Effects Model
201
5.1
General Formulation of the Extended Model
. 202
5.1.1
Estimation and Computational Methods
. 202
5.1.2
The GLS model
. 203
5.1.3
Decomposing the Within-Group Variance-Covariance
Structure
. 205
5.2
Variance Functions for Modeling Heteroscedasticity
. 206
5.2.1
varFunc classes in nlme
. 208
5.2.2
Using varFunc classes with
Ime
. 214
5.3
Correlation Structures for Modeling Dependence
. 226
5.3.1
Serial Correlation Structures
. 226
5.3.2
Spatial Correlation Structures
. 230
5.3.3
corStruct classes in nlme
. 232
5.3.4
Using corStruct Classes with
Ime
. 239
5.4
Fitting Extended Linear Models with gls
. 249
5.5
Chapter Summary
. 266
Exercises
. 267
II Nonlinear Mixed-Effects Models
271
6
NLME Models: Basic Concepts and Motivating
Examples
273
6.1
LME Models vs. NLME Models
. 273
6.2
Indomethicin Kinetics
. 277
6.3
Growth of Soybean Plants
. 287
6.4
Clinical Study of
Phénobarbital
Kinetics
. 294
6.5
Chapter Summary
. 300
Exercises
. 301
7
Theory and Computational Methods for NLME Models
305
7.1
The NLME Model Formulation
. 306
7.1.1
Single-Level of Grouping
. 306
7.1.2
Multilevel NLME Models
. 309
7.1.3
Other NLME Models
. 310
7.2
Estimation and Inference in NLME Models
. 312
7.2.1
Likelihood Estimation
. 312
7.2.2
Inference and Predictions
. 322
7.3
Computational Methods
. 324
7.4
Extending the Basic NLME Model
. 328
xiv Contents
7.4.1 General
model formulation
. 328
7.4.2
Estimation and Computational Methods
. 329
7.5
An Extended Nonlinear Regression Model
. 332
7.5.1
General Model Formulation
. 333
7.5.2
Estimation and Computational Methods
. 334
7.6
Chapter Summary
. 336
8
Fitting Nonlinear Mixed-Effects Models
337
8.1
Fitting Nonlinear Models in
S
with nls and nlsList
. 338
8.1.1
Using the nls Function
. 338
8.1.2
Self-Starting Nonlinear Model Functions
. 342
8.1.3
Separate Nonlinear Fits by Group: The nlsList
Function
. 347
8.2
Fitting Nonlinear Mixed-Effects Models with nlme
. 354
8.2.1
Fitting Single-Level nlme Models
. 354
8.2.2
Using Covariates with nlme
. 365
8.2.3
Fitting Multilevel nlme Models
. 385
8.3
Extending the Basic nlme Model
. 391
8.3.1
Variance Functions in nlme
. 391
8.3.2
Correlation Structures in nlme
. 395
8.3.3
Fitting Extended Nonlinear Regression Models
with gnls
. 401
8.4
Chapter Summary
. 409
Exercises
. 410
References
415
A Data Used in Examples and Exercises
423
A.I Alfalfa—Split-Plot Experiment on Varieties of Alfalfa
. 425
A.2 Assay—Bioassay on Cell Culture Plate
. 425
A.3 BodyWeight—Body Weight Growth in Rats
. 427
A.4 Cefamandole—Pharmacokinetics of Cefamandole
. 427
A.5 CO2—Carbon Dioxide Uptake
. 428
A.6 Dialyzer—High-Flux Hemodialyzer
. 429
A.7 DNase—Assay Data for the Protein DNase
. 429
A.8 Earthquake—Earthquake Intensity
. 430
A.9 ergoStool—Ergometrics Experiment with Stool Types
. 431
A.10 Gluco^—Glucose Levels Following Alcohol
Ingestion
. 432
A.ll IGF—Radioitnmunoassay of IGF-I Protein
. 433
A.12 Indometh—Indomethicin Kinetics
. 433
A.13 Loblolly—Growth of Loblolly Pine Trees
. 434
A.14 Machines—Productivity Scores for Machines and Workers
. 435
A.
15
Oats—Split-plot Experiment on Varieties of Oats
. 435
A.16 Orange—Growth of Orange Trees
. 436
A.lTOrthodont—Orthodontic Growth Data
. 436
Contents xv
A.18
Ovary
—
Counts of Ovarian Follicles
. 437
A-lDOxboys—Heights of Boys in Oxford
. 437
A.20 Oxide
—
Variability in Semiconductor Manufacturing
. 437
A.21 PBG—Effect of Phenylbiguanide on Blood Pressure
. 438
A.22 PBIB—A Partially Balanced Incomplete Block Design
. . . 439
A.
23
Phenobarb—Phenobarbitol Kinetics
. 440
A.
24
Pixel
—
Pixel Intensity in Lymphnodes
. 440
A.
25
Quinidine
—
Quinidine Kinetics
. 441
A.
26
Rail—Evaluation of Stress in Rails
. 443
A.
27
Soybean
—
Soybean Leaf Weight over Time
. 443
A.28 Spruce
—
Growth of Spruce Trees
. 444
A.29 Theoph—Theophylline Kinetics
. 444
A.
30
Wafer—Modeling of Analog
MOS
Circuits
. 448
A.31
уУЬеаЇг—
Wheat Yield Trials
. 448
S
Functions and Classes
451
ACF
. 451
ACF.lme
. 452
anova.lme
. 453
coef
.
Ime
. 455
coef
.
lmList
. 457
fitted.
Ime
. 458
fixef
. 459
gapply
. 460
getGroups
. 461
gls
. 462
gnls
. 464
groupedData
. 466
gsummary
. 469
intervals
. 471
intervals
.
Ime
. 471
intervals.lmList
. 473
Ime
. 474
lmeControl
. 476
lmList
. 478
logLik
. 479
nlme
. 479
nlmeControl
. 483
nlsList
. 485
pairs
.
Ime
. 486
plot.
Ime
. 488
plot.nfnGroupedData
. 490
plot
.
nmGroupedData
. 492
plot.Variogram
. 494
predict.
Ime
. 495
Contents
qqnorm.lme. 497
ranef. 498
ranef
.Ime
. 499
ranef. lmList. 501
residuals.
Ime .
503
self
Start. 504
self
Start.
default
. 505
self
Start.
formula
. 506
Variogram
. 507
Variogram.lme
. 508
A Collection of Self-Starting Nonlinear Regression
Models
511
C.I SSasymp
—
The Asymptotic Regression Model
. 511
C.I.I Starting Estimates for SSasymp
. 511
C.2 SSasympOff
—
Asymptotic Regression with an Offset
. 512
C.2.1 Starting Estimates for SSasympOff
. 512
C.3 SSasympOrig
—
Asymptotic Regression Through the Origin
513
C.3.1 Starting Estimates for SSasympOrig
. 513
C.4 SSbiexp—Biexponential Model
. 514
C.4.1 Starting Estimates for SSbiexp
. 515
C.5 SSf ol—First-Order Compartment Model
. 516
C.S.I Starting Estimates for SSf ol
. 516
C.6 SSfpl
—
Four-Parameter Logistic Model
. 517
C.6.1 Starting Estimates for SSfpl
. 518
C.7 SSlogis—Simple Logistic Model
. 519
C.7.1 Starting Estimates for SSlogis
. 519
C.8 SSmicmen—Michaelis-Menten Model
. 520
C.e.l Starting Estimates for SSmicmen
. 521
Index
523 |
| any_adam_object | 1 |
| author | Pinheiro, José C. Bates, Douglas M. |
| author_facet | Pinheiro, José C. Bates, Douglas M. |
| author_role | aut aut |
| author_sort | Pinheiro, José C. |
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| building | Verbundindex |
| bvnumber | BV035988622 |
| callnumber-first | Q - Science |
| callnumber-label | QA76 |
| callnumber-raw | QA76.73.S15 |
| callnumber-search | QA76.73.S15 |
| callnumber-sort | QA 276.73 S15 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | ST 601 |
| ctrlnum | (OCoLC)247850539 (DE-599)DNB992999715 |
| dewey-full | 005.133 |
| dewey-hundreds | 000 - Computer science, information, general works |
| dewey-ones | 005 - Computer programming, programs, data, security |
| dewey-raw | 005.133 |
| dewey-search | 005.133 |
| dewey-sort | 15.133 |
| dewey-tens | 000 - Computer science, information, general works |
| discipline | Informatik Mathematik |
| format | Book |
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| id | DE-604.BV035988622 |
| illustrated | Illustrated |
| indexdate | 2024-07-20T10:27:36Z |
| institution | BVB |
| isbn | 9781441903174 |
| language | English |
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| physical | XVIII, 528 S. graph. Darst. |
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| publisher | Springer |
| record_format | marc |
| series2 | Statistics and computing |
| spelling | Pinheiro, José C. Verfasser aut Mixed-effects models in S and S-PLUS José Pinheiro ; Douglas Bates New York, NY Springer 2000 XVIII, 528 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Statistics and computing Gemischtes Modell - S <Programmiersprache> - S-PLUS Gemischtes Modell (DE-588)4156565-4 gnd rswk-swf S-PLUS (DE-588)4321162-8 gnd rswk-swf S Programmiersprache (DE-588)4234472-4 gnd rswk-swf Gemischtes Modell (DE-588)4156565-4 s S Programmiersprache (DE-588)4234472-4 s S-PLUS (DE-588)4321162-8 s 1\p DE-604 DE-604 Bates, Douglas M. Verfasser aut text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3253909&prov=M&dok_var=1&dok_ext=htm Inhaltstext Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018881383&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Pinheiro, José C. Bates, Douglas M. Mixed-effects models in S and S-PLUS Gemischtes Modell - S <Programmiersprache> - S-PLUS Gemischtes Modell (DE-588)4156565-4 gnd S-PLUS (DE-588)4321162-8 gnd S Programmiersprache (DE-588)4234472-4 gnd |
| subject_GND | (DE-588)4156565-4 (DE-588)4321162-8 (DE-588)4234472-4 |
| title | Mixed-effects models in S and S-PLUS |
| title_auth | Mixed-effects models in S and S-PLUS |
| title_exact_search | Mixed-effects models in S and S-PLUS |
| title_full | Mixed-effects models in S and S-PLUS José Pinheiro ; Douglas Bates |
| title_fullStr | Mixed-effects models in S and S-PLUS José Pinheiro ; Douglas Bates |
| title_full_unstemmed | Mixed-effects models in S and S-PLUS José Pinheiro ; Douglas Bates |
| title_short | Mixed-effects models in S and S-PLUS |
| title_sort | mixed effects models in s and s plus |
| topic | Gemischtes Modell - S <Programmiersprache> - S-PLUS Gemischtes Modell (DE-588)4156565-4 gnd S-PLUS (DE-588)4321162-8 gnd S Programmiersprache (DE-588)4234472-4 gnd |
| topic_facet | Gemischtes Modell - S <Programmiersprache> - S-PLUS Gemischtes Modell S-PLUS S Programmiersprache |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=3253909&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018881383&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT pinheirojosec mixedeffectsmodelsinsandsplus AT batesdouglasm mixedeffectsmodelsinsandsplus |