Multilevel statistical models:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Chichester
Wiley
2011
|
| Ausgabe: | 4. ed. |
| Schriftenreihe: | Wiley series in probability and statistics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. [333] - 346 |
| Beschreibung: | XXI, 358 S. graph. Darst. |
| ISBN: | 9780470748657 |
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Datensatz im Suchindex
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| adam_text |
Titel: Multilevel statistical models
Autor: Goldstein, Harvey
Jahr: 2011
Contents
Preface xv
Acknowledgements xvii
Notation xix
A general Classification notation and diagram xx
Glossary xxiii
1 An introduction to multilevel modeis 1
1.1 Hierarchically structured data 1
1.2 School effectiveness 3
1.3 Sample survey methods 5
1.4 Repeated measures data 5
1.5 Event history and survival modeis 6
1.6 Discrete response data 7
1.7 Multivariate modeis 7
1.8 Nonlinear modeis 8
1.9 Measurement errors 9
1.10 Cross classifications and multiple membership structures 9
1.11 Factor analysis and structural equation modeis 10
1.12 Levels of aggregation and ecological fallacies 10
1.13 Causality 11
1.14 The latent normal transformation and missing data 13
1.15 Other texts 14
1.16 Acaveat 14
2 The 2-level model 15
2.1 Introduction 15
2.2 The 2-level model 17
2.3 Parameter estimation 19
2.3.1 The variance components model 19
2.3.2 The general 2-level model with random coefficients 21
2.4 Maximum likelihood estimation using iterative generalised Ieast
Squares (IGLS) 22
2.5 Marginal modeis and generalised estimating equations (GEE) 25
viii CONTENTS
2.6 Residuais 25
2.7 The adequacy of ordinary least Squares estimates 27
2.8 A 2-level example using longitudinal educational
achievement data 28
2.8.1 Checking for outlying units 30
2.8.2 Model checking using estimated residuals 31
2.9 General model diagnostics 32
2.10 Higher level explanatory variables and compositional effects 34
2.11 Transforming to normality 36
2.12 Hypothesis testing and confidence intervals 39
2.12.1 Fi xed parameters 39
2.12.2 Random parameters 41
2.12.3 Hypothesis testing for non-nested modeis 42
2.12.4 Inferences for residual estimates 43
2.13 Bayesian estimation using Markov Chain Monte Carlo (MCMC) 45
2.13.1 Gibbs sampling 47
2.13.2 Metropolis-Hastings (MH) sampling 48
2.13.3 ConvergenceofMCMCchains 48
2.13.4 Making inferences 49
2.13.5 An example 50
2.14 Data augmentation 55
Appendix 2.1 The general structure and maximum likelihood
estimation for a multilevel model 57
Appendix 2.2 Multilevel residuals estimation 60
2.2.1 Shrunken estimates 60
2.2.2 Delta method estimators for the covariance
matrix of residuals 61
Appendix 2.3 Estimation using profile and extended likelihood 63
Appendix 2.4 The EM algorithm 65
Appendix 2.5 MCMC sampling 67
2.5.1 Gibbs sampling 67
2.5.2 Metropolis-Hastings (MH) sampling 70
2.5.3 Hierarchical centring 71
2.5.4 Orthogonaiisation ofthe explanatory
variables and parameter expansion 72
3 3-level modeis and more complex hierarchical structures 73
3.1 Complex variance structures 73
3.1.1 Partitioning the variance and intra-unit correlation 79
3.1.2 Variances for subgroups defined at level 1 80
3.1.3 Variance as a function of predicted value 83
3.1.4 Variances for subgroups defined at higher levels 85
3.2 A 3-level complex Variation model example 85
3.3 Parameter constraints 88
3.4 Weighting units 90
CONTENTS ix
3.4.1 Maximum likelihood estimation with weights 91
3.4.2 Weighted MCMC estimation 92
3.5 Robust (sandwich) estimators and jacknifing 93
3.6 The bootstrap 95
3.6.1 The fully nonparametric bootstrap 95
3.6.2 The fully parametric bootstrap 95
3.6.3 The iterated parametric bootstrap and bias correction 96
3.6.4 The residuals bootstrap 98
3.7 Aggregate level analyses 101
3.7.1 Inferences about residuals from aggregate level analyses 103
3.8 Meta analysis 104
3.8.1 Aggregate and mixed level analysis 106
3.8.2 Defining origin and scale 107
3.8.3 An example: meta analysis of class size data 107
3.8.4 Practical issues in meta analysis 108
3.9 Design issues 109
4 Multilevel modeis for discrete response data 111
4.1 Generalised linear modeis 111
4.2 Proportions as responses 112
4.3 Examples 115
4.3.1 A study of contraceptive use 115
4.3.2 Modelling school segregation 117
4.4 Models for multiple response categories 119
4.5 Models for counts 122
4.6 Ordered responses 123
4.7 Mixed discrete-continuous response modeis 124
4.8 A latent normal model for binary responses 126
4.9 Partitioning Variation in discrete response modeis 127
4.9.1 Model linearisation (Method A) 128
4.9.2 Simulation (Method B) 128
4.9.3 A binary linear model (Method C) 129
4.9.4 A latent variable approach (Method D) 129
4.9.5 An example of VPC calculations 130
Appendix 4.1 Multilevel generalised linear model estimation 132
4.1.1 Approximate quasilikelihood estimates 132
4.1.2 Differentials for some discrete response modeis 134
Appendix 4.2 Maximum likelihood estimation for multilevel
generalised linear modeis 135
4.2.1 Simulated maximum likelihood estimation 135
4.2.2 Residuals 138
4.2.3 Cross classifications and multiple
membership modeis 139
4.2.4 Computing issues 139
4.2.5 Maximum likelihood estimation via quadrature 140
x CONTENTS
Appendix 4.3 MCMC estimation for generalised linear modeis 142
4.3.1 Metropolis-Hastings (MH) sampling 142
4.3.2 Latent variable modeis for binary data 142
4.3.3 Proportions as responses 144
Appendix 4.4 Bootstrap estimation for multilevel generalised linear
modeis 145
4.4.1 The iterated bootstrap 145
5 Models for repeated measures data 147
5.1 Repeated measures data 147
5.2 A 2-level repeated measures model 148
5.3 A polynomial model example for adolescent growth and the
prediction of adult height 149
5.4 Modelling an autocorrelation structure at level 1 153
5.5 A growth model with autocorrelated residuals 154
5.6 Multivariate repeated measures modeis 156
5.7 Scaling across time 156
5.8 Cross-over designs 157
5.9 Missingdata 157
5.10 Longitudinal discrete response data 159
6 Multivariate multilevel data 161
6.1 Introduction 161
6.2 The basic 2-level multivariate model 162
6.3 Rotation designs 164
6.4 A rotation design example using Science Survey test scores 164
6.5 Informative response selection: subject choice in examinations 167
6.6 Multivariate structures at higher levels and future predictions 168
6.7 Multivariate responses at several levels 170
6.7.1 Fitting responses at several levels using random data
augmentation 171
6.8 Principal components analysis 172
6.9 Multiple discriminant analysis 173
Appendix 6.1 MCMC algorithm for a multivariate normal response
model with constraints 175
6.1.1 Constraints among parameters 176
7 Latent normal modeis for multivariate data 179
7.1 The normal multilevel multivariate model 179
7.2 Sampling binary responses 180
7.3 Sampling ordered categorical responses 180
7.4 Sampling unordered categorical responses 182
7.5 Sampling count data 182
7.6 Sampling continuous non-normal data 183
CONTENTS xi
7.7 Sampling the level 1 and level 2 covariance matrices 183
7.8 Model fit 184
7.9 Partially ordered data 185
7.10 Hybrid normal/ordered variables 185
7.10.1 Ordered data with known thresholds 186
7.11 Discussion 187
8 Multilevel factor analysis, structural equation
and mixture modeis 189
8.1 A 2-stage 2-level factor model 189
8.2 A general multilevel factor model 191
8.3 MCMC estimation for the factor model 192
8.3.1 A 2-level factor example 193
8.4 Structural equation modeis 195
8.5 Discrete response multilevel structural equation modeis 197
8.6 More complex hierarchical latent variable modeis 198
8.7 Multilevel mixture modeis 198
9 Nonlinear multilevel modeis 201
9.1 Introduction 201
9.2 Nonlinear functions of linear components 201
9.3 Estimating population means 202
9.4 Nonlinear functions for variances and covariances 203
9.5 Examples of nonlinear growth and nonlinear level 1 variance 204
Appendix 9.1 Nonlinear model estimation 207
9.1.1 Modelling variances and covariances as
nonlinear functions 208
10 Multilevel modelling in sample surveys 211
10.1 Sample survey structures 211
10.2 Population structures 212
10.2.1 Superpopulations 212
10.2.2 Finite population inference 213
10.3 Small area estimation 214
10.3.1 Information at domain level only 215
10.3.2 Longitudinal data 216
10.3.3 Multivariate responses 216
11 Multilevel event history and survival modeis 217
11.1 Introduction 217
11.2 Censoring 218
11.3 Hazard and survival functions 218
11.4 Parametric proportional hazard modeis 219
11.5 The semiparametric Cox model 220
11.6 Tied observations 221
xii CONTENTS
11.7 Repeated events proportional hazard modeis 222
11.8 Example using birth interval data 222
11.9 Log duration modeis 223
11.9.1 Censoreddata 225
11.9.2 Infinite durations 226
11.10 Examples with birth interval data and children's activity episodes 227
11.11 The grouped discrete time hazards model 229
11.11.1 A 2-level discrete time event history model for
repeated events 232
11.11.2 Partnership data example 234
11.11.3 General discrete time event history modeis 234
11.12 Discrete time latent normal event history modeis 237
11.12.1 Censoreddata 238
11.12.2 Missingdata 238
11.12.3 Information about the timing of events in an interval 238
11.12.4 Modelling the threshold parameters and time
varying covariates 239
11.12.5 An example using partnership durations 240
12 Cross-classified data structures 243
12.1 Random cross classifications 243
12.2 A basic cross-classified model 245
12.3 Examination results for a cross Classification of schools 247
12.4 Interactions in cross classifications 248
12.5 Cross classifications with one unit per cell 248
12.6 Multivariate cross-classified modeis 249
12.7 A general notation for cross Classification 249
12.8 MCMC estimation in cross-classified modeis 250
Appendix 12.1 IGLS estimation for cross-classified data 252
12.1.1 An efficient IGLS algorithm 252
12.1.2 Computational considerations 253
13 Multiple membership modeis 255
13.1 Multiple membership structures 255
13.2 Notation and classifications for multiple membership structures 256
13.3 An example of Salmonella infection 257
13.4 A repeated measures multiple membership model 258
13.5 Individuais as higher level units 259
13.5.1 Example of research grantawards 261
13.6 Spatial modeis 261
13.7 Missing identification modeis 263
Appendix 13.1 MCMC estimation for multiple membership modeis 265
14 Measurement errors in multilevel modeis 267
14.1 A basic measurement error model 267
CONTENTS xiii
14.2 Moment-based estimators 268
14.2.1 Measurement errors in level 1 variables 268
14.2.2 Measurement errors in higher level variables 269
14.3 A 2-level example with measurement error at both levels 271
14.4 Multivariate responses 273
14.5 Nonlinear modeis 274
14.6 Measurement errors for discrete explanatory variables 274
14.7 MCMC estimation for measurement error modeis 275
Appendix 14.1 Measurement error estimation 277
14.1.1 Moment based estimators for a basic 2-level
model 277
14.1.2 Parameter estimation 278
14.1.3 Random coefficients for explanatory
variables measured with error 279
14.1.4 Nonlinear modeis 279
14.1.5 MCMC estimation for measurement error
modeis: continuous variables 280
14.1.6 MCMC estimation for measurement error
modeis: discrete variables 281
14.1.7 A latent normal model for discrete and
continuous variables with measurement errors 284
15 Smoothing modeis for multilevel data 285
15.1 Introduction 285
15.2 Smoothing estimators 285
15.2.1 Regression splines 285
15.3 Smoothing splines 286
15.4 Semiparametric smoothing modeis 287
15.5 Multilevel smoothing modeis 290
15.6 General multilevel semiparametric smoothing modeis 292
15.7 Generalised linear modeis 293
15.8 An example 293
15.9 Conclusions 298
16 Missing data, partially observed data and multiple
Imputation 301
16.1 Introduction 301
16.2 Creating a completed dataset 302
16.3 Joint modelling for missing data 304
16.4 A 2-level model with responses of different types at both levels 305
16.4.1 Sampling level 1 non-normal responses 305
16.4.2 Sampling level 2 non-normal responses 306
16.5 Multiple imputation 306
16.6 A Simulation example of multiple imputation for missing data 307
16.7 Longitudinal data with attrition 308
xiv CONTENTS
16.8 Partially known data values 309
16.8.1 An application to record linkage 310
16.8.2 Estimating a probability distribution using record
linkage weights 311
16.9 Conclusions 312
17 Multilevel modeis with correlated random effects 315
17.1 Introduction 315
17.2 Non-independence of level 2 residuals 315
17.3 MCMC estimation for non-independent level 2 residuals 317
17.3.1 Sampling the level 2 covariance matrix 318
17.3.2 Sampling the level 2 residuals 319
17.4 Adaptive proposal distributions in MCMC estimation 319
17.5 MCMC estimation for non-independent level 1 residuals 320
17.5.1 A 2-level model formulated as a Single level model
with non-independent residuals 321
17.6 Modelling the level 1 variance as a function of explanatory
variables with random effects 321
17.7 Discrete responses with correlated random effects 322
17.7.1 The probit ordered response model where the variance
is a function of explanatory variables with random effects 323
17.8 Calculating the DIC statistic 324
17.9 A growth dataset 325
17.10 Conclusions 326
18 Software for multilevel modelling 329
18.1 Software packages 329
References 333
Author index 347
Subject index 351 |
| any_adam_object | 1 |
| author | Goldstein, Harvey 1939-2020 |
| author_GND | (DE-588)115041699 |
| author_facet | Goldstein, Harvey 1939-2020 |
| author_role | aut |
| author_sort | Goldstein, Harvey 1939-2020 |
| author_variant | h g hg |
| building | Verbundindex |
| bvnumber | BV039635772 |
| classification_rvk | MR 2100 QH 234 SK 840 |
| classification_tum | EDU 100f MAT 622f |
| ctrlnum | (OCoLC)700336705 (DE-599)GBV63027536X |
| discipline | Pädagogik Soziologie Mathematik Wirtschaftswissenschaften |
| edition | 4. ed. |
| format | Book |
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| id | DE-604.BV039635772 |
| illustrated | Illustrated |
| indexdate | 2024-12-06T09:03:58Z |
| institution | BVB |
| isbn | 9780470748657 |
| language | English |
| lccn | 2010023377 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-024485798 |
| oclc_num | 700336705 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-91 DE-BY-TUM DE-19 DE-BY-UBM DE-188 DE-20 DE-473 DE-BY-UBG DE-634 |
| owner_facet | DE-91G DE-BY-TUM DE-91 DE-BY-TUM DE-19 DE-BY-UBM DE-188 DE-20 DE-473 DE-BY-UBG DE-634 |
| physical | XXI, 358 S. graph. Darst. |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | Wiley |
| record_format | marc |
| series2 | Wiley series in probability and statistics |
| spelling | Goldstein, Harvey 1939-2020 Verfasser (DE-588)115041699 aut Multilevel statistical models Harvey Goldstein 4. ed. Chichester Wiley 2011 XXI, 358 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Wiley series in probability and statistics Literaturverz. S. [333] - 346 Mathematisches Modell Sozialwissenschaften Sozialwissenschaften (DE-588)4055916-6 gnd rswk-swf Statistische Analyse (DE-588)4116599-8 gnd rswk-swf Multivariate Analyse (DE-588)4040708-1 gnd rswk-swf Pädagogik (DE-588)4044302-4 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Statistisches Modell (DE-588)4121722-6 gnd rswk-swf Kontextanalyse (DE-588)4129240-6 gnd rswk-swf Social sciences Mathematical models Social sciences Research Methodology Educational tests and measurements Mathematical models Statistisches Modell (DE-588)4121722-6 s Kontextanalyse (DE-588)4129240-6 s DE-604 Sozialwissenschaften (DE-588)4055916-6 s Mathematisches Modell (DE-588)4114528-8 s 1\p DE-604 Pädagogik (DE-588)4044302-4 s 2\p DE-604 3\p DE-604 4\p DE-604 Statistische Analyse (DE-588)4116599-8 s 5\p DE-604 Multivariate Analyse (DE-588)4040708-1 s 6\p DE-604 Erscheint auch als Online-Ausgabe 978-0-470-97339-4 Erscheint auch als Online-Ausgabe, PDF 978-0-470-97340-0 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024485798&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 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 5\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 6\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Goldstein, Harvey 1939-2020 Multilevel statistical models Mathematisches Modell Sozialwissenschaften Sozialwissenschaften (DE-588)4055916-6 gnd Statistische Analyse (DE-588)4116599-8 gnd Multivariate Analyse (DE-588)4040708-1 gnd Pädagogik (DE-588)4044302-4 gnd Mathematisches Modell (DE-588)4114528-8 gnd Statistisches Modell (DE-588)4121722-6 gnd Kontextanalyse (DE-588)4129240-6 gnd |
| subject_GND | (DE-588)4055916-6 (DE-588)4116599-8 (DE-588)4040708-1 (DE-588)4044302-4 (DE-588)4114528-8 (DE-588)4121722-6 (DE-588)4129240-6 |
| title | Multilevel statistical models |
| title_auth | Multilevel statistical models |
| title_exact_search | Multilevel statistical models |
| title_full | Multilevel statistical models Harvey Goldstein |
| title_fullStr | Multilevel statistical models Harvey Goldstein |
| title_full_unstemmed | Multilevel statistical models Harvey Goldstein |
| title_short | Multilevel statistical models |
| title_sort | multilevel statistical models |
| topic | Mathematisches Modell Sozialwissenschaften Sozialwissenschaften (DE-588)4055916-6 gnd Statistische Analyse (DE-588)4116599-8 gnd Multivariate Analyse (DE-588)4040708-1 gnd Pädagogik (DE-588)4044302-4 gnd Mathematisches Modell (DE-588)4114528-8 gnd Statistisches Modell (DE-588)4121722-6 gnd Kontextanalyse (DE-588)4129240-6 gnd |
| topic_facet | Mathematisches Modell Sozialwissenschaften Statistische Analyse Multivariate Analyse Pädagogik Statistisches Modell Kontextanalyse |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024485798&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT goldsteinharvey multilevelstatisticalmodels |