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Verbeke G., Molenberghs G. Linear Mixed Models for Longitudinal Data
Verbeke G., Molenberghs G.  Linear Mixed Models for Longitudinal Data









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: Linear Mixed Models for Longitudinal Data

: Verbeke G., Molenberghs G.

:

This book provides a comprehensive treatment of linear mixed models for continuous longitudinal data. Next to model formulation, this book puts major emphasis on exploratory data analysis for all aspects of the model. Several variations to the conventional linear mixed model are discussed. Most analyses were done with the Mixed procedure of the SAS software package, however, other commercially available packages are discussed as well. Great care has been taken in presenting the data analyses in a software-independent fashion.


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ed2k: ed2k stats

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: 579

: 15.06.2005

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Age-related macular degeneration      427
Age-related macular degeneration, coefficient of multiple determination      437
Akaike information criterion (AIC)      see Information criteria
Ancillary statistic      377
Ancova      221
anova      221 229
Autoregressive AR(1)      see Covariance structure
Available case analysis      222 227 263
Balanced data      119 215
BALANCED object      see OSWALD
Baltimore Longitudinal Study of Aging (BLSA)      1012
Baltimore Longitudinal Study of Aging (BLSA), hearing data      see Hearing data
Baltimore Longitudinal Study of Aging (BLSA), prostate data      see Prostate data
Banded      see Covariance structure
Bayesian methods      41 46 69 470
Bayesian methods, empirical Bayes estimation (EB)      see Random effects
Bayesian methods, hierarchical Bayes model      172
Bayesian methods, posterior distribution      78 176
Bayesian methods, posterior mean      78 176
Bayesian methods, posterior probability      175 177
Bayesian methods, prior distribution      78
Bayesian methods, shrinkage      8082 85
Best linear unbiased prediction (BLUP)      80
Bivariate outcome      405
Blood pressure data      405411
Bozdogan information criterion (CAIC)      see Information criteria
BY statement      357
Case deletion      see Global influence
Class statement      96 483
Classification of profiles      see Heterogeneity model
Cluster analysis      see Heterogeneity model
Coefficient of multiple determination, random effect      431 438
Coefficient of multiple determination, residual      433 438
Coefficient of multiple determination, subject-specific      see Subject-specific profiles
Colorectal cancer      427129
Colorectal cancer, coefficient of multiple determination      438
Complete case analysis      211 222223 227
Complete data      see Missing data
Complete data set      241
Compound symmetry      25 68 117 118
Compound symmetry, Greenhouse Geiser      120
Compound symmetry, Huynh Feldt      120
Compound symmetry, random intercepts      see Random-intercepts model
Computing time      47 97 118
Conditional independence      see Covariance structure
Conditional linear mixed model      194197
Conditional linear mixed model, empirical Bayes estimation (EB)      195
Conditional linear mixed model, estimation      195
Conditional linear mixed model, fixed-effects approach      198200
Conditional linear mixed model, inference      195
Conditional linear mixed model, justification      196
Conditional linear mixed model, maximum likelihood estimation (ML)      195
Conditional linear mixed model, paired t-test      196
Conditional linear mixed model, restricted maximum likelihood estimation (REML)      195
CONTRAST statement      101 104 410
CONTRAST statement, chisq option      101
Convergence problems      see Estimation problems
Cook's distance      see Influence analysis
Covariance structure      62 64 117 121 240 265
Covariance structure, ante-dependence      232
Covariance structure, autoregressive AR(1)      99 122 252 258 388 452 499
Covariance structure, banded      99 388
Covariance structure, compound symmetry      25 68 99 117 118 120 253 260 262 302307 326 389
Covariance structure, conditional independence      26 85 159
Covariance structure, correlation structure      34 419
Covariance structure, exchangeable      253 260 388
Covariance structure, exploration      33 34
Covariance structure, heterogeneous      99
Covariance structure, independence      106 256 389
Covariance structure, measurement error      27 28 117 129 135 237 241 270 416 502 504
Covariance structure, model building      125 132
Covariance structure, patterned      388
Covariance structure, preliminary      474
Covariance structure, random effects      28 135 416
Covariance structure, residual      2629 128 132 271 416
Covariance structure, residual, REPEATED statement      98
Covariance structure, residuals      160
Covariance structure, serial correlation      27 28 128132 135150 241 306 416 449 498
Covariance structure, serial correlation, exponential      28 100 139 142
Covariance structure, serial correlation, Gaussian      28 100 129 139 142 270
Covariance structure, simple      99
Covariance structure, spatial      100
Covariance structure, starting values      131
Covariance structure, stationarity      126 127 142
Covariance structure, Toeplitz      99 250 262
Covariance structure, unstructured      99 242 247 353 389
Covariance structure, variance function      25 33 53 127 130 131 201
Coverage probability      382
Cross-sectional component      189 194
Degrees of freedom, F-test      see F-test
Degrees of freedom, Satterthwaite method      57 112 486
Degrees of freedom, t-test      see t-test
Delta method      286 357 432 451 454
design considerations      391 104
Design considerations, comparing power distributions      395 397404
Design considerations, designed power      391 394397
Design considerations, dropout mechanism      397
Design considerations, intentionally incomplete      393
Design considerations, power      392393
Design considerations, power distribution      394404
Design considerations, random-effects distribution      87
Design considerations, realized power      391 394 104
Design considerations, sampling methods      396 104
Design considerations, under expected dropout      394397
Design matrix      215 241 247 249 252 259
Deviance      242
Discriminant analysis      see Heterogeneity model
Dose-response model      412
Dropout      see Missing data
Dropout model      235 236 269 271 280 297 302 314 326 328
Dropout model, direct variables      465466 469
Dropout model, increment      272 312 315 321 326 328 463 465466 469
Dropout model, size      272 312 315 326
Dropout rate      280
Efficiency      see Design considerations
EM algorithm      173 177 329 387390
EM algorithm, E step      175 388
EM algorithm, ECM algorithm      387
EM algorithm, ECME algorithm      387
EM algorithm, GEM algorithm      389
EM algorithm, heterogeneity model      173177
EM algorithm, linear mixed model      47
EM algorithm, M step      175 388
EM algorithm, missing data      210 222 232 240 258 277 302 376
EM algorithm, rate of convergence      47 389
EM algorithm, versus Newton Raphson      173
Empirical Bayes estimation (EB)      see Random effects
Empirical variance      see Fixed effects
Error contrasts      see REML
ESTIMATE statement      101 104 410
ESTIMATE statement, alpha= option      102
ESTIMATE statement, cl option      102
Estimation problems      5054 439442
Estimation problems, model misspecification      5254
Estimation problems, model parameterization      131
Estimation problems, small variance components      5052
Exchangeable      see Covariance structure
Exercise bike data      498
Exponential serial correlation      see Serial correlation
F-test, degrees of freedom      57 112 393
F-test, fixed effects      see Fixed effects
F-test, noncentral      393 396
F-test, PROC MIXED versus PROC GLM      119
F-test, random effects      see Random effects
Fisher scoring      50 103 131 385
Fixed effects      24 224 241 385
Fixed effects, F-test      56 112 115 392
Fixed effects, general linear hypothesis      56 58 392
Fixed effects, general linear hypothesis, CONTRAST statement      101
Fixed effects, inference      5563 133
Fixed effects, local influence      see Local influence
Fixed effects, LR test      62 392
Fixed effects, maximum likelihood      42
Fixed effects, MODEL statement      96
Fixed effects, multivariate test      119
Fixed effects, parameterization in SAS      114117
Fixed effects, restricted maximum likelihood      45
Fixed effects, robust inference      6162 121
Fixed effects, robust inference, empirical variance      61 474
Fixed effects, robust inference, sandwich estimator      61 88
Fixed effects, t-test      56 111 112 115 392
Fixed effects, versus random effects      198200
Fixed effects, Wald test      56 112
Fractional polynomials      20 137139 478479
Full data      see Missing data
Gaussian serial correlation      see Serial correlation
General linear hypothesis      see Fixed effects
Generalized estimating equations      125 218 229 391
Gibbs sampling      390
Global influence      314 460 162
Global influence, case deletion      153 165 298 314 320 325 457
Global influence, one-step approach      152 159
Global influence, versus local influence      153 466470
Greenhouse Geiser      see Compound symmetry
Growth curves      248
Growth data      1617 240268 388
Growth data, complete data analysis      240256
Growth data, incomplete data analysis, frequentist analysis      256257
Growth data, incomplete data analysis, likelihood analysis      257267
Growth data, incomplete data analysis, missinguess process      267268
Growth data, MLwiN      489493
Growth data, multilevel model      489493
Hannan and Quinn information criterion (HQC)      see Information criteria
Hearing data      14
Hearing data, conditional linear mixed model      197200
Hearing data, contaminated data      191 193
Hearing data, empirical Bayes estimation (EB)      192
Hearing data, fixed effects versus random effects      198200
Hearing data, linear mixed model      190 191
Hearing data, misspecified cross-sectional component      191193
Heat shock study      411419
Heights of schoolgirls      16
Heights of schoolgirls, classification of subjects      184187
Heights of schoolgirls, cluster analysis      184187
Heights of schoolgirls, discriminant analysis      184187
Heights of schoolgirls, heterogeneity model      184187
Heights of schoolgirls, linear mixed model      183184
Heights of schoolgirls, two-stage approach      183
Henderson's mixed model equations      79
Hepatitis B vaccination      470 484
Hepatitis B vaccination, semi-variogram      473
Hessian matrix      see Information matrix
Heterogeneity model      85 87 90 91 169 171172
Heterogeneity model, classification      169 177 182 186
Heterogeneity model, cluster analysis      177 181 186
Heterogeneity model, discriminant analysis      177 181
Heterogeneity model, EM algorithm      173177
Heterogeneity model, empirical Bayes estimation (EB)      176
Heterogeneity model, goodness-of-fit      178 179 181 185
Heterogeneity model, identifiability      174
Heterogeneity model, Kolmogorov Smirnov test      178 181 186
Heterogeneity model, likelihood ratio test      91 178
Heterogeneity model, Newton Raphson      173
Heterogeneity model, number of components      91 178179 181 185
Heterogeneity model, posterior probability      175 177
Heterogeneity model, Shapiro Wilk test      179 181 186
Hierarchical Bayes model      see Bayesian methods
Hierarchical model      24 41 52 65 67 69 77 117
Hierarchical model, versus marginal model      52 65 117
Homogeneity model      85 90 172
Homogeneity model, goodness-of-fit      178179 181 185
Hot deck imputation      see Imputation
Huynh Feldt      see Compound symmetry
ID statement      97
Identifiability      174 231 278 280
Identifiable parameter      216 (see also Estimable parameter)
Identifying restrictions      see Pattern-mixture model
Ignorable analysis      239240 266
Ignorable missing data      see Missing data
Imputation      222
Imputation, Buck      225
Imputation, conditional mean      224 226
Imputation, hot deck      224 226
Imputation, last observation carried forward (LOCF)      224 226
Imputation, mean      224
Imputation, multiple      222 336 339 344 350352 359 371 373
Imputation, multiple, estimation      338
Imputation, multiple, estimation task      337
Imputation, multiple, F-test      339
Imputation, multiple, hypothesis testing      338339
Imputation, multiple, imputation task      337
Imputation, multiple, modeling task      337
Imputation, multiple, proper      344
Imputation, multiple, variance      338
Imputation, simple      211212 222226
Imputation, single      223
Imputation, unconditional mean      225
Incomplete data      see Missing data
Independence model      see Covariance structure
Influence analysis      457470
Influence analysis, Cook's distance      151 457
Influence analysis, global      305 (see Global influence hat-matrix diagonal)
Influence analysis, leverage      151 304
Influence analysis, local      see Local influence
Influence graph      see Local influence
Information criteria      7476 129 409
Information criteria, Akaike (AIC)      74 106 107 406
Information criteria, Bozdogan (CAIC)      74 107
Information criteria, Hannan and Quinn (HQIC)      74 107
Information criteria, ML versus REML      75 107
Information criteria, Schwarz (SBC)      74 106 107 406
Information matrix      64 88
Information matrix, expected      103 131 132 376 378 382
Information matrix, Hessian      50 131
Information matrix, naive      380
Information matrix, observed      103 131 132 376 378 385
Intentionally incomplete designs      393
Intraclass correlation      25 68 86 260
Kolmogorov Smirnov test      178 181 186
kurtosis      318
Last observation carried forward      see Imputation
Latent variable      328
Leverage      see Influence analysis
Likelihood displacement      see Local influence
Likelihood function      104 106
Likelihood function, complete data      378
Likelihood function, factorization      217
Likelihood function, full data      217
Likelihood function, maximum likelihood      42
Likelihood function, objective function      105
Likelihood function, observed data      258 318 387
Likelihood function, restricted maximum likelihood      46
Likelihood ratio test      239 375
Likelihood ratio test, asymptotic null distribution      6973 91 178 254
Likelihood ratio test, fixed effects      62 247 392
Likelihood ratio test, heterogeneity model      91 178
Likelihood ratio test, missing data      375
Likelihood ratio test, missing data mechanism      310 313 320 324 459 511
Likelihood ratio test, ML versus REML      63 66 69
Likelihood ratio test, pattern specific      283
Likelihood ratio test, random effects      6973 133 408
Likelihood ratio test, variance components      65 106 133 262 392
Likelihood ratio test, Wilk's Lambda      119
Likelihood-based frequentist inference      385
Linear mixed model      2329
Local influence      153 158 298300
Local influence, case-weight perturbation      156
Local influence, cutoff value      161 162
Local influence, fixed effects      161 162 303
Local influence, index plot      160 161 163
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