Mixed models: theory and applications with R
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| Main Author: | |
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| Format: | Book |
| Language: | English |
| Published: |
Hoboken, NJ
Wiley
2013
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| Edition: | 2. ed. |
| Series: | Wiley series in probability and statistics
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | XXVII, 717 S. graph. Darst. 25 cm |
| ISBN: | 9781118091579 |
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| 300 | |a XXVII, 717 S. |b graph. Darst. |c 25 cm | ||
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Record in the Search Index
| _version_ | 1804151519557189632 |
|---|---|
| adam_text | Titel: Mixed models
Autor: Demidenko, Eugene
Jahr: 2013
Contents
Preface xvii
Preface to the Second Edition xix
R Software and Functions xx
Data Sets xxii
Open Problems in Mixed Models xxiii
1 Introduction: Why Mixed Models? 1
1.1 Mixed effects for clustered data 2
1.2 ANOVA, variance components, and the mixed model 4
1.3 Other special cases of the mixed effects model 6
1.4 Compromise between Bayesian and frequentist approaches 7
1.5 Penalized likelihood and mixed effects 9
1.6 Healthy Akaike information criterion 11
1.7 Penalized smoothing 13
1.8 Penalized polynomial fitting 16
1.9 Restraining parameters, or what to eat 18
1.10 Ill-posed problems, Tikhonov regularizaron, and mixed effects ... 20
1.11 Computerized tomography and linear image reconstruction 23
1.12 GLMM for PET 26
1.13 Maple leaf shape analysis 29
1.14 DNA Western blot analysis 31
1.15 Where does the wind blow? 33
1.16 Software and books 36
viii Contents
37
1.17 Summary points
MLE for the LME Model
2.1 Example: weight versus height
2.1.1 The first R script
2.2 The model and log-likelihood functions 45
2.2.1 The model ^
2.2.2 Log-likelihood functions 48
2.2.3 Dimension-reduction formulas 49
2.2.4 Profile log-likelihood functions 53
2.2.5 Dimension-reduction GLS estimate 55
2.2.6 Restricted maximum likelihood 56
2.2.7 Weight versus height (continued) 59
2.3 Balanced random-coefficient model 60
2.4 LME model with random intercepts 64
2.4.1 Balanced random-intercept model 67
2.4.2 How random effect affects the variance of MLE 71
2.5 Criterion for MLE existence 72
2.6 Criterion for the positive defimteness of matrix D 74
2.6.1 Example of an invalid LME model 75
2.7 Pre-estimation bounds for variance parameters 77
2.8 Maximization algorithms 79
2.9 Derivatives of the log-likelihood function 81
2.10 Newton-Raphson algorithm 82
2.11 Fisher scoring algorithm 85
2.11.1 Simplified FS algorithm . 86
2.11.2 Empirical FS algorithm 86
2.11.3 Variance-profile FS algorithm 87
2.12 EM algorithm 88
2.12.1 Fixed-point algorithm 92
2.13 Starting point 93
2.13.1 FS starting point 93
2.13.2 FP starting point 94
2.14 Algorithms for restricted MLE 95
2.14.1 Fisher scoring algorithm 95
2.14.2 EM algorithm %
2.15 Optimization on nonnegative definite matrices 96
2.15.1 How often can one hit the boundary? 97
2.15.2 Allow matrix D to be not nonnegative definite 98
2.15.3 Force matrix D to stay nonnegative definite 103
2.15.4 Matrix D reparameterization 104
2.15.5 Criteria for convergence 105
2.16 lmeFS and lme in R 107
2.17 Appendix: proof of the existence of MLE Ill
2.18 Summary points H4
Statistical Properties of the LME Model 117
3.1 Introduction -yyj
Contents ix
3.2 Identifiability of the LME model 117
3.2.1 Linear regression with random coefficients 119
3.3 Information matrix for variance parameters 120
3.3.1 Efficiency of variance parameters for balanced data 129
3.4 Profile-likelihood confidence intervals 131
3.5 Statistical testing of the presence of random effects 133
3.6 Statistical properties of MLE 137
3.6.1 Small-sample properties 137
3.6.2 Large-sample properties 140
3.6.3 ML and RML are asymptotically equivalent 144
3.7 Estimation of random effects 145
3.7.1 Implementation in R 148
3.8 Hypothesis and membership testing 151
3.8.1 Membership test 152
3.9 Ignoring random effects 154
3.10 MINQUE for variance parameters 157
3.10.1 Example: linear regression 158
3.10.2 MINQUE for o*2 160
3.10.3 MINQUE for D* 162
3.10.4 Linear model with random intercepts 165
3.10.5 MINQUE for the balanced model 165
3.10.6 lmevarMINQUE function 166
3.11 Method of moments 166
3.11.1 lmevarMM function 171
3.12 Variance least squares estimator 171
3.12.1 Unbiased VLS estimator 173
3.12.2 Linear model with random intercepts 174
3.12.3 Balanced design 174
3.12.4 VLS as the first iteration of ML 175
3.12.5 lmevarUVLS function 175
3.13 Projection on EI)+ space 176
3.14 Comparison of the variance parameter estimation 176
3.14.1 lmesim function 179
3.15 Asymptotically efficient estimation for ß 180
3.16 Summary points 181
4 Growth Curve Model and Generalizations 185
4.1 Linear growth curve model 185
4.1.1 Known matrix D 187
4.1.2 Maximum likelihood estimation 189
4.1.3 Method of moments for variance parameters 192
4.1.4 Two-stage estimation 196
4.1.5 Special growth curve models 196
4.1.6 Unbiasedness and efficient estimation for ß 200
4.2 General linear growth curve model 201
4.2.1 Example: Calcium supplementation for bone gain 202
4.2.2 Variance parameters are known 204
4.2.3 Balanced model 207
X
Contents
4.2.4 Likelihood-based estimation
4.2.5 MM estimator for variance parameters
4.2.6 Two-stage estimator and asymptotic properties 214
4.2.7 Analysis of misspecification 215
4.3 Linear model with linear covariance structure 219
4 3.1 Method of maximum likelihood 220
999
4.3.2 Variance least squares
4.3.3 Statistical properties 223
4.3.4 LME model for longitudinal autocorrelated data 224
4.3.5 Multidimensional LME model 229
4.4 Robust linear mixed effects model 233
4.4.1 Robust estimation of the location parameter with estimated
cr and 235
4.4.2 Robust linear regression with estimated threshold 238
4.4.3 Robust LME model 239
4.4.4 Alternative robust functions 239
4.4.5 Robust random effect model 240
4.5 Appendix: derivation of the MM estimator 241
4.6 Summary points 242
5 Meta-analysis Model 245
5.1 Simple meta-analysis model 246
5.1.1 Estimation of random effects 248
5.1.2 Maximum likelihood estimation 248
5.1.3 Quadratic unbiased estimation for cr2 253
5.1.4 Statistical inference 260
5.1.5 Robust/median meta-analysis 266
5.1.6 Random effect coefficient of determination 271
5.2 Meta-analysis model with covariates 273
5.2.1 Maximum likelihood estimation 274
5.2.2 Quadratic unbiased estimation for cr2 277
5.2.3 Hypothesis testing 278
5.3 Multivariate meta-analysis model 278
5.3.1 The model 280
5.3.2 Maximum likelihood estimation 283
5.3.3 Quadratic estimation of the heterogeneity matrix 285
5.3.4 Test for homogeneity 288
5.4 Summary points 289
6 Nonlinear Marginal Model 291
6.1 Fixed matrix of random effects 292
293
295
296
297
298
298
6.1.1 Log-likelihood function
6.1.2 nls function in R
6.1.3 Computational issues of nonlinear least squares
6.1.4 Distribution-free estimation
6.1.5 Testing for the presence of random effects
6.1.6 Asymptotic properties
6.1.7 Example: log-Gompertz growth curve 299
Contents xi
6.2 Varied matrix of random effects 305
6.2.1 Maximum likelihood estimation 305
6.2.2 Distribution-free variance parameter estimation 308
6.2.3 GEE and iteratively reweighted least squares 309
6.2.4 Example: logistic curve with random asymptote 310
6.3 Three types of nonlinear marginal models 316
6.3.1 Type I nonlinear marginal model 317
6.3.2 Type II nonlinear marginal model 319
6.3.3 Type III nonlinear marginal model 319
6.3.4 Asymptotic properties under distribution misspecification . . 320
6.4 Total generalized estimating equations approach 321
6.4.1 Robust feature of total GEE 323
6.4.2 Expected Newton—Raphson algorithm for total GEE 323
6.4.3 Total GEE for the mixed effects model 324
6.4.4 Total GEE for the LME model 324
6.4.5 Example (continued): log-Gompertz curve 325
6.4.6 Photodynamic tumor therapy 326
6.5 Summary points 328
7 Generalized Linear Mixed Models 331
7.1 Regression models for binary data 332
7.1.1 Approximate relationship between logit and probit 336
7.1.2 Computation of the logistic-normal integral 338
7.1.3 Gauss-Hermite numerical quadrature for multidimensional in¬
tegrals in R 350
7.1.4 Log-likelihood and its numerical properties 352
7.1.5 Unit step algorithm 353
7.2 Binary model with subject-specific intercept 355
7.2.1 Consequences of ignoring a random effect 357
7.2.2 ML logistic regression with a fixed subject-specific intercept 358
7.2.3 Conditional logistic regression 359
7.3 Logistic regression with random intercept 362
7.3.1 Maximum likelihood 362
7.3.2 Fixed sample likelihood approximation 368
7.3.3 Quadratic approximation 371
7.3.4 Laplace approximation to the likelihood 371
7.3.5 VARLINK estimation 374
7.3.6 Beta-binomial model 376
7.3.7 Statistical test of homogeneity 378
7.3.8 Asymptotic properties 381
7.4 Probit model with random intercept 382
7.4.1 Laplace and PQL approximations 382
7.4.2 VARLINK estimation 383
7.4.3 Heckman method for the probit model 383
7.4.4 Generalized estimating equations approach 384
7.4.5 Implementation in R 386
7.5 Poisson model with random intercept 386
7.5.1 Poisson regression for count data 387
Contents
7.5.2 Clustered count data
7.5.3 Fixed intercepts
7.5.4 Conditional Poisson regression
7.5.5 Negative binomial regression
7.5.6 Normally distributed intercepts
7.5.7 Exact GEE for any distribution
7.5.8 Exact GEE for balanced count data
7.5.9 Heckman method for the Poisson model
7.5.10 Tests for overdispersion
7.5.11 Implementation in R
7.6 Random intercept model: overview
7.7 Mixed models with multiple random effects
7.7.1 Multivariate Laplace approximation
7.7.2 Logistic regression
7.7.3 Probit regression
7.7.4 Poisson regression
7.7.5 Homogeneity tests
7.8 GLMM arid simulation methods
7.8.1 General form of GLMM via the exponential family
7.8.2 Monte Carlo for ML
7.8.3 Fixed sample likelihood approach
7.9 GEE for clustered marginal GLM
7.9.1 Variance least squares
7.9.2 Limitations of the GEE approach
7.9.3 Marginal or conditional model?
7.9.4 Implementation in R
7.10 Criteria for MLE existence for a binary model
7.11 Summary points
Nonlinear Mixed Effects Model 433
8.1 Introduction 433
8.2 The model 434
8.3 Example: height of girls and boys 437
8.4 Maximum likelihood estimation 439
8.5 Two-stage estimator 442
8.5.1 Maximum likelihood estimation 445
8.5.2 Method of moments 445
8.5.3 Disadvantage of two-stage estimation 446
8.5.4 Further discussion 446
8.5.5 Two-stage method in the presence of a common parameter . 447
8.6 First-order approximation . 448
8.6.1 GEE and MLE . . . . . . . . . . .448
8.6.2 Method of moments and VLS 449
8.7 Lindstrom—Bates estimator 45O
8.7.1 What if matrix D is not positive definite? 452
8.7.2 Relation to the two-stage estimator 452
8.7.3 Computational aspects of penalized least squares 453
8.7.4 Implementation in R: the function nlme 454
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Contents xiii
8.8 Likelihood approximations 456
8.8.1 Linear approximation of the likelihood at zero 456
8.8.2 Laplace and PQL approximations 457
8.9 One-parameter exponential model 459
8.9.1 Maximum likelihood estimator 459
8.9.2 First-order approximation 460
8.9.3 Two-stage estimator 461
8.9.4 Lindstrom-Bates estimator 463
8.10 Asymptotic equivalence of the TS and LB estimators 466
8.11 Bias-corrected two-stage estimator 468
8.12 Distribution misspecification 470
8.13 Partially nonlinear marginal mixed model 473
8.14 Fixed sample likelihood approach 474
8.14.1 Example: one-parameter exponential model 475
8.15 Estimation of random effects and hypothesis testing 476
8.15.1 Estimation of the random effects 476
8.15.2 Hypothesis testing for the NLME model 477
8.16 Example (continued) 478
8.17 Practical recommendations 480
8.18 Appendix: Proof of theorem on equivalence 481
8.19 Summary points 484
9 Diagnostics and Influence Analysis 487
9.1 Introduction 487
9.2 Influence analysis for linear regression 488
9.3 The idea of infinitesimal influence 491
9.3.1 Data influence 491
9.3.2 Model influence 492
9.4 Linear regression model 493
9.4.1 Influence of the dependent variable 494
9.4.2 Influence of the continuous explanatory variable 495
9.4.3 Influence of the binary explanatory variable 497
9.4.4 Influence on the predicted value 497
9.4.5 Case or group deletion 498
9.4.6 R code 500
9.4.7 Influence on regression characteristics 501
9.4.8 Example 1: Women s body fat 503
9.4.9 Example 2: gypsy moth study 507
9.5 Nonlinear regression model 510
9.5.1 Influence of the dependent variable on the LSE 510
9.5.2 Influence of the explanatory variable on the LSE 510
9.5.3 Influence on the predicted value 511
9.5.4 Influence of case deletion 511
9.5.5 Example 3: logistic growth curve model 512
9.6 Logistic regression for binary outcome 515
9.6.1 Influence of the covariate on the MLE 516
9.6.2 Influence on the predicted probability 516
9.6.3 Influence of the case deletion on the MLE 517
xiv Contents
517
9.6.4 Sensitivity to ^
9.6.5 Example: Finney data
9.7 Influence of correlation structure
9.8 Influence of measurement error
9.9 Influence analysis for the LME model
9.9.1 Example: Weight versus height
9.10 Appendix: MLE derivative with respect to a2 534
9.11 Summary points
10 Tumor Regrowth Curves 539
10.1 Survival curves 541
10.2 Double-exponential regrowth curve 543
10.2.1 Time to regrowth, TR 546
10.2.2 Time to reach specific tumor volume, T# 547
10.2.3 Doubling time, Td
10.2.4 Statistical model for regrowth 548
10.2.5 Variance estimation for tumor regrowth outcomes 549
10.2.6 Starting values 550
10.2.7 Example: chemotherapy treatment comparison 551
10.3 Exponential growth with fixed regrowth time 557
10.3.1 Statistical hypothesis testing 558
10.3.2 Synergistic or supra-additive effect 558
10.3.3 Example: combination of treatments 559
10.4 General regrowth curve 563
10.5 Double-exponential transient regrowth curve 564
10.5.1 Example: treatment of cellular spheroids 570
10.6 Gompertz transient regrowth curve 571
10.6.1 Example: tumor treated in mice 572
10.7 Summary points 574
11 Statistical Analysis of Shape 577
11.1 Introduction 577
11.2 Statistical analysis of random triangles 579
11.3 Face recognition 582
11.4 Scale-irrelevant shape model 583
11.4.1 Random effects scale-irrelevant shape model 585
11.4.2 Scale-irrelevant shape model on the log scale 586
11.4.3 Fixed or random size? 587
11.5 Gorilla vertebrae analysis 587
11.6 Procrustes estimation of the mean shape 589
11.6.1 Polygon estimation 592
11.6.2 Generalized Procrustes model 592
11.6.3 Random effects shape model 593
11.6.4 Random or fixed (Procrustes) effects model? 594
11.6.5 Maple leaf analysis 594
11.7 Fourier descriptor analysis 596
11.7.1 Analysis of a star shape 59g
11.7.2 Random Fourier descriptor analysis 602
Contents xv
11.7.3 Potato project 604
11.8 Summary points 605
12 Statistical Image Analysis 607
12.1 Introduction 607
12.1.1 What is a digital image? 608
12.1.2 Image arithmetic 609
12.1.3 Ensemble and repeated measurements 609
12.1.4 Image and spatial statistics 610
12.1.5 Structured and unstructured images 610
12.2 Testing for uniform lighting 610
12.2.1 Estimating light direction and position 612
12.3 Kolmogorov-Smirnov image comparison 614
12.3.1 Kolmogorov-Smirnov test for image comparison 614
12.3.2 Example: histological analysis of cancer treatment 615
12.4 Multinomial statistical model for images 618
12.4.1 Multinomial image comparison 620
12.5 Image entropy 621
12.5.1 Reduction of a gray image to binary 623
12.5.2 Entropy of a gray image and histogram equalization 623
12.6 Ensemble of unstructured images 625
12.6.1 Fixed-shift model 626
12.6.2 Random-shift model 628
12.6.3 Mixed model for gray images 631
12.6.4 Two-stage estimation 633
12.6.5 Schizophrenia MRI analysis 635
12.7 Image alignment and registration 638
12.7.1 Affine image registration 641
12.7.2 Weighted sum of squares 642
12.7.3 Nonlinear transformations 643
12.7.4 Random registration 643
12.7.5 Linear image interpolation 644
12.7.6 Computational aspects 645
12.7.7 Derivative-free algorithm for image registration 646
12.7.8 Example: clock alignment 647
12.8 Ensemble of structured images 650
12.8.1 Fixed affine transformations 650
12.8.2 Random affine transformations 651
12.9 Modeling spatial correlation 652
12.9.1 Toeplitz correlation structure 654
12.9.2 Simultaneous estimation of variance and transform parameters 656
12.10 Summary points 658
xvi Contents
13 Appendix: Useful Facts and Formulas 661
13.1 Basic facts of asymptotic theory 661
13.1.1 Central Limit Theorem 661
13.1.2 Generalized Slutsky theorem 662
13.1.3 Pseudo-maximum likelihood 664
13.1.4 Estimating equations approach and the sandwich formula . . 665
13.1.5 Generalized estimating equations approach 667
13.2 Some formulas of matrix algebra 668
13.2.1 Some matrix identities 668
13.2.2 Formulas for generalized matrix inverse 668
13.2.3 Vec and vech functions; duplication matrix 669
13.2.4 Matrix differentiation 670
13.3 Basic facts of optimization theory 672
13.3.1 Criteria for unimodality 673
13.3.2 Criteria for global optimum 674
13.3.3 Criteria for minimum existence 674
13.3.4 Optimization algorithms in statistics 675
13.3.5 Necessary condition for optimization and criteria for conver¬
gence 678
References 681
Index 711
|
| any_adam_object | 1 |
| author | Demidenko, Eugene 1948- |
| author_GND | (DE-588)1042255792 |
| author_facet | Demidenko, Eugene 1948- |
| author_role | aut |
| author_sort | Demidenko, Eugene 1948- |
| author_variant | e d ed |
| building | Verbundindex |
| bvnumber | BV041409377 |
| classification_rvk | QH 233 |
| ctrlnum | (OCoLC)896214388 (DE-599)HBZHT017682475 |
| dewey-full | 519.538 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.538 |
| dewey-search | 519.538 |
| dewey-sort | 3519.538 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV041409377 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:56:07Z |
| institution | BVB |
| isbn | 9781118091579 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-026856705 |
| oclc_num | 896214388 |
| open_access_boolean | |
| owner | DE-20 DE-739 |
| owner_facet | DE-20 DE-739 |
| physical | XXVII, 717 S. graph. Darst. 25 cm |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | Wiley |
| record_format | marc |
| series2 | Wiley series in probability and statistics |
| spelling | Demidenko, Eugene 1948- Verfasser (DE-588)1042255792 aut Mixed models theory and applications with R Eugene Demidenko 2. ed. Hoboken, NJ Wiley 2013 XXVII, 717 S. graph. Darst. 25 cm txt rdacontent n rdamedia nc rdacarrier Wiley series in probability and statistics Includes bibliographical references and index Gemischtes Modell (DE-588)4156565-4 gnd rswk-swf R Programm (DE-588)4705956-4 gnd rswk-swf Varianzanalyse (DE-588)4187413-4 gnd rswk-swf Gemischtes Modell (DE-588)4156565-4 s R Programm (DE-588)4705956-4 s DE-604 Varianzanalyse (DE-588)4187413-4 s 1\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026856705&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 | Demidenko, Eugene 1948- Mixed models theory and applications with R Gemischtes Modell (DE-588)4156565-4 gnd R Programm (DE-588)4705956-4 gnd Varianzanalyse (DE-588)4187413-4 gnd |
| subject_GND | (DE-588)4156565-4 (DE-588)4705956-4 (DE-588)4187413-4 |
| title | Mixed models theory and applications with R |
| title_auth | Mixed models theory and applications with R |
| title_exact_search | Mixed models theory and applications with R |
| title_full | Mixed models theory and applications with R Eugene Demidenko |
| title_fullStr | Mixed models theory and applications with R Eugene Demidenko |
| title_full_unstemmed | Mixed models theory and applications with R Eugene Demidenko |
| title_short | Mixed models |
| title_sort | mixed models theory and applications with r |
| title_sub | theory and applications with R |
| topic | Gemischtes Modell (DE-588)4156565-4 gnd R Programm (DE-588)4705956-4 gnd Varianzanalyse (DE-588)4187413-4 gnd |
| topic_facet | Gemischtes Modell R Programm Varianzanalyse |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026856705&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT demidenkoeugene mixedmodelstheoryandapplicationswithr |