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Demidenko E. — Mixed Models: Theory and Applications
Demidenko E. — Mixed Models: Theory and Applications

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Название: Mixed Models: Theory and Applications

Автор: Demidenko E.

Аннотация:

In spite of the fact that a number of books have been published on this subject recently, this volume presents rigorous and self-contained coverage of the topic. The goal of the book is to fill the gap in the existing literature. Most of the available texts on mixed models concentrate on the discussion of basic properties of the models with a large number of examples. In contrast, this book provides in-depth mathematical coverage of mixed models' statistical properties and numerical algorithms. State-of-the-art methodologies are discussed, among them the linear mixed-effects model, the growth curve model, the generalized growth curve model, robust models, models with linear covariance structures, models for binary and count clustered data, the generalized estimation equation approach, nonlinear mixed models, and diagnostics. Special attention is given to algorithms and their implementations. Several appendices make the text self-contained. Applications include tumor regrowth and statistical analysis of shapes and images.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2004

Количество страниц: 704

Добавлена в каталог: 19.05.2006

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
A posteriori      25 28
A priori      24 27
Absolute lower bound      439 456 462
Adaptive Gauss — Hermite quadrature      346 361
ADIFOR      629
Affine image registration      624
AIC (Akaike information criterion)      2 13 15
Alignment      622
AMM (Asymptotic Method of Moments) estimator      170
Amygdala-hippocampal complex      621
Angular criterion      663
ANOVA (analysis of variance)      5 6 42 170 567
AR (autoregression)      226 518
Asymptotic covariance matrix      81 116 122 181 195 252 294 308 394 647 649
Asymptotically efficient      143 179 180 220 225 239 291 304 327 360 416 478 647
Attenuation      27 335 354 422
Balanced data      49 62 68 72 74 82 94 129 178 217 229 273 394
Bar-influence      498 516 530
Bayesian      2 8 22 23 42 60 148 181 585
Bending energy      15
Beta-binomial      373 428
Between (inter)-clusters variance      1 42 78 184 433
Bias correction      459 461 464
Biased estimating equations      649
Binary image      597 604 607
Binary model      330 351 359 400 405
Bit      607 609
BLGC (Balanced Linear Growth Curve) model      197
BLUE (Best Linear Unbiased Estimator)      54 207
BLUP (Best Linear Unbiased Predictor)      148 591
Case deletion      481 484 493 498 505 509 511 523 530
Cauchy inequality      218 265 280 313 358 440 466 645
Cell kinetics      532
Cellular spheroid      299 534 561
Chemotherapy      543
Chi-distribution      134 136 230 262 375 572 605 616 640
Cholesky decomposition      100 116 233 295 411 470 652
Clonogenic cells      536 547 566
CLT (Central Limit Theorem)      143 144 180 263 643
Cluster deletion      523 526
Clustered data      1 2 42 47 114 329 382 384 414 661
Commutation matrix      123 653
Complimentary log-log      334
Compound symmetry      418
Conditional logistic regression      356
Conditional model      22 420 430
Conditional Poisson regression      387
Confidence interval      58 131 151 181 262 267 469 472
Consistent estimator      142 145 179 181 308 327 415 459 466 467
Constrained optimization      99 110 659
Convergence criteria      110 295 405 663
Cook's distance      483 485 525 530
Coregistration      623
Count data      383 388 391
Covariance matrix      7 29 44 47 122 139 304
Covh matrix      123
Cramer — Rao bound      129 178 252 441
Cross-influence      497
CT (Computerized Tomography)      26
Data influence      482 486 530
DE (Double-Exponential) regrowth curve      538
Deficient matrix      123 184 220 634
DET (Double-Exponential Transient) regrowth curve      559
Deterministic asymptotics      143 268 298 308 646 649
Difference matrix      29
Dimension-reduction formula      10 28 52 67 89 148 209 226 294 394 448 591 651
Distribution misspecification      320 390 465 467
Distribution-free      7 49 96 117 157 171 191 223 223 255 286 296 307 313 327 491 576
Distribution-free estimation      117 157 296 307
Dose-response relationship      534
Doubling time      540
DUD algorithm      629
Duplication matrix      123 407 470 652
Efficiency      129 132 181 219 232 245 264 303 304 308 314 378 415 439 467
EFS (Empirical Fisher Scoring) algorithm      88 271 360 392 406 661
EGEE (Exact GEE)      393
EM (Expectation-Maximization) algorithm      31 32 44 75 90 98 115 253 411 443 659
Empirical information      86
ENR (Expected Newton — Raphson) algorithm      324
Ensemble      33 44 356 595 598 610 612 631
Epidemiology      20
EPP (Entropy Per Pixel)      609 641
Errors-in-variables      118 518 580
Estimability      118
Estimated GLS      117 139 179 200 645
Exchangeable correlation      418
Existence      55 74 95 111 255 296 350 354 422 429 455 462 658
Expected information      86
Explanatory variable      14 43 48 196 201 249 292 330 384 482 483 488—490 492 493 504 518 529 617 619 648
F-test      137 152 181 375 397 408 430 472 591 599
Face recognition      572
Fast-growing tumor      536
First-order condition      109 110 116 158 258 448 450
First-stage model      184 201 245 441 452 479 576 616 626
Fixed effects model      5 42 54 79 187 352 588
Fixed-effects estimator      54 67
Fixed-shift model      612
Fixed-size shape      574 577 580
FOA (First-order approximation) estimator      445
Fourier descriptor      585 588 589 592 594
FP (Fixed-Point) algorithm      94 97 98 191 212 275 369 402 659
Frequentist      2 8 42
FS (Fisher Scoring) algorithm      32 81 86—89 96 98 115 222 242 252 275 284 307 350 379 393 659 660
FSL (Fixed Simulated Likelihood) approximation      365 411 470 480 614
Full-profile likelihood      58 89 189
Gamma distribution      10 263 373
Gauss — Hermite quadrature      344 365 411 480
GDET (General Double-Exponential Transient) regrowth curve      559
GEE (Generalized Estimating Equations) approach      307—309 321 380 414 418 422 430 446 650
GLGC (General Linear Growth Curve) model      201
GLM (Generalized Linear Model)      330 410 415
GLMM (Generalized Linear Mixed Model)      30 44 329 330 414 421 430 452 611 617
Global minimum      110 657
GLS (Generalized Least Squares)      53 58 59 63 67 72 441 443—445 450 457 458 462 464 474 475 584 619 645
GN (Gauss — Newton) algorithm      307 407 417 442 448 587 629 660
Gompertz curve      298
Gradient      80 657 663
Gray image      572 597 600 603 607 609 611 616 639
Grayscale format      597 600 603
Group deletion      494
GT (Gompertz Transient) regrowth curve      563
HAIC (Healthy Akaike Information Criterion)      13
Heckman method      380 396
hessian      12 81 83 85 86 141 222 251 274 284 349 350 357 358 366 384 387 400 412 504 509 656 657 663
Heterogeneity      1 36 248 252 261 283 285 290 311 398 533 546 585
Hierarchical model      1 4 8 24 42 184 316 373 479 576 616 626 662
Histogram equalization      609 640
Homogeneity test      248 262 278 290
Huber function      236 241
Hyperparameter      8 42
Idempotent matrix      137 168 211 469
Identifiability      117 119
Iid (independent and identically distributed)      2 62 142 235 242 326 358 373 455 459 569 589 613 634 643 644 646
Ill-posed problem      2 11 22 43
Image histogram      601 605 606
Image processing      596
Image reconstruction      2 23 25 26 30 43 595
Improved Laplace approximation      342 362 428
In vitro      299 535 556 566
In vivo      299 300 531 536 556 561 563 566
Infinitesimal influence (I-influence)      481 486 488 492 495 504 505 519 522 530
Influence analysis      153 482 483 489 490 503 522
Influential observation      481 489 496 509 529
Information matrix      81 86 293 439
Inverse link function      330
Inverse problem      23
IRLS (Iteratively Reweighted Least Squares) algorithm      237 241 242 308 420 446 661
Isotropic shape      580
Knonecker product      49 85 88 124 162 234 403 583 600 634 654
Kolmogorov — Smirnov test      601
Kuhn — Tucker condition      110 285 663
Kullback Leibler information      13
LA (Laplace Approximation)      12 341 343 368 402 452 454 471
Lagrange function      149 158 205 258
Landmark      568 573 578 583 585 594 631 641
Large-sample properties      144 178
LB (Lindstrom — Bates) method      447 450 460 480
Leaf analysis      33 591
Levenberg — Maquardt algorithm      295 442
Leverage      481 484 492 503 505 509 515 522 527 530
LGC (Linear Growth Curve) model      183 187
Likelihood displacement      482 487 529
Likelihood ratio test      135 606
Line S-Plus function      134 153 229
Linear image interpolation      627
Link function      330
Link-approximation      337 338
LME (Linear Mixed Effects) model      4 7 17 18 48 66 74 77 117 183 241 447 522 577
LMLCS (Linear Model with Linear Covariance Structure)      220 246
Local influence      482 487 490 522 529
Location parameter      235 237 269
Log-gamma distribution      388 391
Log-Gompertz curve      300 303 315 326 469 534
Logistic growth curve      310 311 436
Logistic regression      68 248 331 332 334 335 337 352 353
Logistic-normal integral      337
logit      335 350 365 373 428 612 641
Longitudinal data      1 4 66 183 184 221 225 246 329 415 430 433 531 536 543 565
LS (least squares)      27 29 466 493 504 506 543 630
M-estimation      180 236 268 293 648
MA (Moving Average)      225
MAP (Maximum A Posteriori) estimator      24 25
Marginal model      291 293 312 315 328
Matrix derivative      317 654
Maximum absolute error.      336
Mean shape      568 575 580 585 587 592
Measurement error      118 518
Membership test      150 571 575 590 622
Meta-analysis      7 88 211 213 247 249 255 263 268 272 273 281 289 374
MINQUE (Minimum Norm Quadratic Unbiased Estimator)      96 157
Misclassification      482 485 492 504 509 511 515 530
Misspecification      215 245 292 390 432 468
ML (Maximum Likelihood)      10 11 25 31 45 51 74 187 208 238 273 282 304 355 442 605 616 632 637
MM (Method of Moments)      140 166 170 175 178 191 192 195 214 243 257 288 297 318 443 570 653
MMFE (Method of Moments Fixed Effects) estimator      195 214
Model influence      482 487 492
Moore — Penrose Generalized Matrix Inverse      54 55 78 123 194 296 651
Morphology      568
MRF (Markov Random Field)      633
MRI (magnetic resonance imaging)      596 614 620
MSE (mean squared error)      178 259 455 462 624 633 639 642
Multidimensionality      20
Multilevel mixed model      1 25 36 44 90 221
Multinomial distribution      604
Multivariate meta-analysis      230 247 282 289 290
Negative binomial regression      387
Nested model      13 66 90 230
NLME (Nonlinear Mixed Effects Model)      432 438 439 472 479
Nlme S-Plus function      474 562
NLS (Nonlinear Least Squares)      293 295 316 442 447 451
Nonlinear regression      23 40 87 110 267 292 296 311 315 327 432 442 451 464 466 475 503 541 601 629 657
Nonnegative definite matrix      48 99
Nonstandard hypothesis testing      134
NR (Newton — Raphson) algorithm      31 80 82 83 109 115 190 209 245 251 283 324 336 350 357 369 386 403 659 660
Nuisance parameters      54 55 68 114 119 201 204 218 296 352 353 356 379 399 460 574 577 580 581 594 613 646
Numerical quadrature      242 344 400
Odds ratio      332
OLS (Ordinary Least Squares)      14 46 53 250 273 315 350 385 443 482 483 488 489 494 518 529 584 622 644
One-probit approximation      335
Oscillation      562 564
Overdispersion      373 374 376 383 388 394 397 417
Overspecification      105 216
Panel data      1 7 42 66 114 330 383
Parent-model      486
Parsimonious model      533
Penalized least squares      19 23 25 28 181 447 451 454 471 479
Penalized likelihood      2 11 13 15 18 22 25 33 42 370 383 403 414 429
Perturbation formula      82 189 283 403
PET (Positron Emission Tomography)      30 43 623 642
Poisson regression      31 43 69 334 383 385 388 392 406 410 430
Polygon shape      582 583
Pooled variance      161 211 244 296 307 442
Population-averaged      4 13 35 42 47 291 306 327 359 371 393 431 433 472 479 567 616 627 642
Positive definite matrix      45 48 51
PQL (Penalized Quasi-Likelihood)      369 379 392 405 453 480
Precision matrix      57 228 234 401 405 410
Probit model      331 332 378 380 405 521
Procrustes shape model      579 583 585
Profile-likelihood confidence interval      132 230
Projection      26 30 43 64 104 137 176 286 491 587
Pseudo-MLE      318 380 647 650
Pseudo-model      445 453 456
Q-test      247 264 277 289 290
Quadratic-logistic growth curve      437
Quiescent cells      536
Radiation dose      534 538 560
Radiosensitivity parameter      534 538 542 560 564
Radius function      589
Random affine transformation      633
Random effects model      5 42 55 247 289 291 398 429 577 578 594
Random Fourier descriptor      34 589 592 594
Random registration      626
Random shape      575 577 584 587
Random triangles      569
Random-coefficient model      61 119 169 184 218 300 594
Random-intercept model      228
Random-shift model      613
Random-size shape      575 577
Random—intercept model      33 47 66 128 155 165 170 174 351 359 378 383 392
Registration      623
Regularization parameter      295
Repeated measurements      1 4 25 37 40 44 221 315 324 334 415 433 596 598
RGB (Red-Green-Blue) format      597 639
Rigid transformation      624
RLGC (Rectangular Linear Growth Curve) model      196
RML (Restricted Maximum Likelihood)      59 63 72 74 98 129 140 146 161 175 181 200 254 290 590
Robust      235 237 241 245 268 272 290 323 328 413 418 649
Rotation      35 567 580 584 587 593 594 624 641
S-Plus      41 81 99 134 153 229 295 308 313 348 414 474 545 546 562
Saddle point      663
SAS      40 81 99 229 485 546
SC (Survival Curve)      534 538 563
Scale-irrelevant shape      576
Scaled covariance matrix      49 201 399 433 444 480 632
Scaled variance      10 29 157 310 315 570 576
Schizophrenia      620
Score equation      31 64 87 190 213 284 308 318 361 392 466 487 510 513 647
Score test      134 227 375 377 398 430
Second-stage model      184 187 196 201 206 207 211 213 218 245 371 440—443 445 479 616 617 633
Semiparametric statistics      18
Sensitivity to measurement error      519
Sensitivity to misclassification      513
Separation plane      423 429 658
Singular matrix      99 105 143 176
Slutsky theorem      180 268 308 644
Small-sample properties      136 139 315
Smoothing      18
Source of variation      4 46 248 576
Spatial autoregression      633
Spatial correlation      634
Star shape      586 588 594
Star-influence      497 530
Starting point      74 96 97 106 115 182 240 328 403 628 659
Stationary point      657
Step length      659
Stochastic asymptotics      144 145 181 200 268 293 308 378
Stopping criteria      110 116 285 663
Structured image      631
Subject-specific      9 33 68 147 196 206 319 351 355 369 371 378 385 422 429 432 441 447 479 534 567 585 612
Synergistic      548 552 566
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