Multilevel statistical models:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
London [u.a.]
Arnold [u.a.]
2003
|
| Ausgabe: | 3. ed. |
| Schriftenreihe: | Kendall's library of statistics
3 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 1. Aufl. u.d.T.: Goldstein, Harvey: Multilevel models in educational and social research |
| Beschreibung: | XV, 253 graph. Darst. |
| ISBN: | 0340806559 9780340806555 |
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Datensatz im Suchindex
| _version_ | 1817681128583069696 |
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| adam_text |
MULTILEVEL
STATISTICAL MODELS
Third Edition
Harvey Goldstein
Institute of Education, University of London, UK
A member of the Hodder Headline Group
LONDON
Distributed in the United States of America by
Oxford University Press Inc , New York
Contents
Preface xi
Acknowledgements xii
Notation xiii
Glossary xvii
1 An Introduction to Multilevel Models 1
1 1 Hierarchically structured data 1
1 2 School effectiveness 2
1 3 Sample survey methods 4
1 4 Repeated measures data 5
1 5 Event history models 6
1 6 Discrete response data 6
1 7 Multivariate models 7
1 8 Nonlinear models 7
1 9 Measurement errors 8
1 10 Random cross-classifications and multiple membership structures 8
1 11 Factor analysis and structural equation models 9
1 12 Levels of aggregation and ecological fallacies 9
1 13 Causality 10
1 14 Other references 12
1 15 A caveat 12
2 The Basic Two-Level Model 13
2 1 Introduction 13
2 2 The 2-level model 15
2 3 Parameter estimation 16
231 The variance components model 16
232 The general 2-level model with random coefficients 18
2 4 Maximum likelihood estimation using Iterative Generalized
Least Squares (IGLS) 19
2 5 Marginal models and Generalized Estimating Equations (GEE) 21
vi Contents
2 6 Residuals 22
2 7 The adequacy of Ordinary Least Squares estimates 23
28A 2-level example using longitudinal educational achievement data 24
281 Checking for outlying units 25
282 Model checking using estimated residuals 27
2 9 General model diagnostics 28
2 10 Higher level explanatory variables and compositional effects 29
2 11 Transforming to Normality 31
2 12 Hypothesis testing and confidence intervals 33
2 12 1 Fixed parameters 33
2 12 2 Random parameters 35
2 12 3 Hypothesis testing for non-nested models 36
2 12 4 Inferences for residual estimates 37
2 13 Bayesian estimation using Markov Chain Monte Carlo (MCMC) 39
2 13 1 Gibbs sampling 40
2 13 2 Metropolis Hastings (MH) sampling 41
2 13 3 Convergence of MCMC chains 41
2 13 4 Making inferences 42
2 13 5 An example 43
2 14 Data augmentation 47
Appendix 2 1 The general structure and maximum likelihood
estimation for a multilevel model 49
Appendix 2 2 Multilevel residuals estimation 52
221 Shrunken estimates 52
222 Delta method estimators for the covariance matrix
of residuals 53
Appendix 2 3 The EM algorithm 55
Appendix 2 4 MCMC sampling 57
241 Gibbs sampling 57
242 Metropolis Hastings (MH) sampling 60
243 Hierarchical centring 61
3 Three-Level Models and More Complex Hierarchical
Structures 63
3 1 Complex variance structures 63
311 Partitioning the variance and intra-unit correlation 68
312 Variances for subgroups defined at level 1 69
313 Variance as a function of predicted value 71
314 Variances for subgroups defined at higher levels 73
32A 3-level complex variation model 74
3 3 Parameter constraints 76
3 4 Weighting units 77
341 Weighted residuals 79
3 5 Robust (sandwich) estimators and jackknifing 80
3 6 The bootstrap 81
361 The fully non-parametric bootstrap 82
362 The fully parametric bootstrap 82
363 The iterated parametric bootstrap and bias correction 83
Contents vii
364 The residuals bootstrap 85
3 7 Aggregate level analyses 87
371 Inferences about residuals from aggregate level analyses 89
3 8 Meta analysis 90
381 Aggregate and mixed level analysis 91
382 Defining origin and scale 92
383 An example: meta analysis of class size data 92
384 Practical issues 93
3 9 Design issues 93
4 Multilevel Models for Discrete Response Data 95
4 1 Generalized linear models 95
4 2 Proportions as responses 96
4 3 An example from a fertility survey 99
4 4 Models for multiple response categories 101
4 5 Models for counts 103
4 6 Ordered responses 104
4 7 Mixed discrete-continuous response models 105
48A latent variable model for binary and ordered responses 107
4 9 Partitioning variation in discrete response models 108
491 An example 110
Appendix 4 1 Generalized linear model estimation 112
411 Approximate quasilikelihood estimates 112
412 Differentials for some discrete response models 114
Appendix 4 2 Maximum likelihood estimation for generalized
linear models 115
421 Simulated maximum likelihood estimation 115
422 Maximum likelihood estimation via quadrature 120
Appendix 4 3 MCMC estimation for generalized linear models 122
431 MH sampling 122
432 Latent variable models for binary data 122
433 Multicategory ordered responses 124
434 Proportions as responses 124
Appendix 4 4 Bootstrap estimation for generalized linear models 125
441 The iterated bootstrap 125
5 Models for Repeated Measures Data 127
5 1 Repeated measures data 127
52A 2-level repeated measures model 128
53A polynomial model example for adolescent growth and the
prediction of adult height 128
5 4 Modelling an autocorrelation structure at level 1 131
55A growth model with autocorrelated residuals 132
5 6 Multivariate repeated measures models 134
5 7 Scaling across time 134
5 8 Cross-over designs 135
5 9 Missing data 135
5 10 Longitudinal discrete response data 137
viii Contents
6 Multivariate Multilevel Data 139
6 1 Introduction 139
6 2 The basic 2-level multivariate model 139
6 3 Rotation designs 141
64A rotation design example using science test scores 142
6 5 Informative subject choice in examinations 144
6 6 Principal components analysis 145
6 7 Multiple discriminant analysis 146
7 Multilevel Factor Analysis and Structural Equation Models 147
71A two-stage 2-level factor model 147
72A general multilevel factor model 149
7 3 MCMC estimation for the factor model 150
731A 2-level factor example 151
7 4 Structural equation models 152
7 5 Discrete response multilevel structural equation models 154
8 Nonlinear Multilevel Models 155
8 1 Introduction 155
8 2 Nonlinear functions of linear components 155
8 3 Estimating population means 156
8 4 Nonlinear functions for variances and covariances 157
8 5 Examples of nonlinear growth and nonlinear level 1 variance 157
8 6 Multivariate nonlinear models 159
Appendix 8 1 Nonlinear model estimation 160
811 Modelling variances and covariances as nonlinear functions 161
812 Likelihood values 162
9 Multilevel Modelling in Sample Surveys 163
9 1 Sample survey structures 163
9 2 Population structures 164
921 Superpopulations 164
922 Finite population inference 165
9 3 Small area estimation 166
931 Information at domain level only 167
932 Longitudinal data 167
933 Multivariate responses 167
10 Multilevel Event History Models 169
10 1 Introduction 169
10 2 Censoring 169
10 3 Hazard and survival functions 170
10 4 Parametric proportional hazard models 171
10 5 The semiparametric Cox model 171
10 6 Tied observations 173
10 7 Repeated measures proportional hazard models 173
10 8 Example using birth interval data 174
Contents ix
10 9 Log duration models 176
10 9 1 Censored data 177
10 9 2 Infinite durations 177
10 10 Examples with birth interval data and children's
activity episodes 178
10 11 The discrete time (piecewise) proportional hazards model 182
10 11 1 A 2-level repeated measures discrete time event
history model 182
10 11 2 Partnership data example 184
10 11 3 General discrete time event history models 185
11 Cross-Classified Data Structures 187
11 1 Random cross-classifications 187
11 2 A basic cross-classified model 190
11 3 Examination results for a cross-classification of schools 191
11 4 Interactions in cross-classifications 192
11 5 Cross-classifications with one unit per cell 192
11 6 Multivariate cross-classified models 193
11 7 A general notation for cross-classifications 193
11 8 MCMC estimation in cross-classified models 194
Appendix 11 1 IGLS estimation for cross-classified data 196
11 1 1 An efficient IGLS algorithm 196
11 1 2 Computational considerations 197
12 Multiple Membership Models 199
12 1 Multiple membership structures 199
12 2 Notation and classifications for multiple membership structures 200
12 3 An example of salmonella infection 201
12 4 A repeated measures multiple membership model 202
12 5 Individuals as higher level units 203
12 6 Spatial models 204
12 7 Missing identification models 205
13 Measurement Errors in Multilevel Models 207
13 1 A basic measurement error model 207
13 2 Moment-based estimators 208
13 2 1 Measurement errors in level 1 variables 208
13 2 2 Measurement errors in higher level variables 209
13 3 A 2-level example with measurement error at both levels 210
13 4 Multivariate responses 212
13 5 Nonlinear models 212
13 6 Measurement errors for discrete explanatory variables 213
13 7 MCMC estimation for measurement error models 214
Appendix 13 1 Measurement error estimation 215
13 1 1 Moment-based estimators for a basic 2-level model 215
13 1 2 Parameter estimation 216
13 1 3 Random coefficients for explanatory variables
measured with error 217
x Contents
13 1 4 Nonlinear models 217
13 1 5 MCMC estimation for measurement error models 217
14 Missing Data in Multilevel Models 219
14 1 A multivariate model for handling missing data 219
14 2 Creating a completed data set 219
14 3 Multiple imputation and error corrections 221
14 4 Discrete variables with missing data 222
14 5 An example with missing data 223
14 6 MCMC estimation for missing data 224
14 7 Informatively missing data 224
15 Software for Multilevel Modelling, Resources and
Further Developments 227
15 1 Software packages and resources 227
15 2 Further developments 227
References 231
Author Index 241
Subject Index 245 |
| 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 | BV017163855 |
| callnumber-first | H - Social Science |
| callnumber-label | H61 |
| callnumber-raw | H61.25 |
| callnumber-search | H61.25 |
| callnumber-sort | H 261.25 |
| callnumber-subject | H - Social Science |
| classification_rvk | MR 2100 QH 234 |
| ctrlnum | (OCoLC)248800109 (DE-599)BVBBV017163855 |
| dewey-full | 519.5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.5 |
| dewey-search | 519.5 |
| dewey-sort | 3519.5 |
| dewey-tens | 510 - Mathematics |
| discipline | Soziologie Mathematik Wirtschaftswissenschaften |
| edition | 3. ed. |
| format | Book |
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| id | DE-604.BV017163855 |
| illustrated | Illustrated |
| indexdate | 2024-12-06T09:03:27Z |
| institution | BVB |
| isbn | 0340806559 9780340806555 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-010347230 |
| oclc_num | 248800109 |
| open_access_boolean | |
| owner | DE-29 DE-N32 DE-739 DE-19 DE-BY-UBM DE-703 DE-11 DE-578 DE-B1533 |
| owner_facet | DE-29 DE-N32 DE-739 DE-19 DE-BY-UBM DE-703 DE-11 DE-578 DE-B1533 |
| physical | XV, 253 graph. Darst. |
| publishDate | 2003 |
| publishDateSearch | 2003 |
| publishDateSort | 2003 |
| publisher | Arnold [u.a.] |
| record_format | marc |
| series | Kendall's library of statistics |
| series2 | Kendall's library of statistics |
| spelling | Goldstein, Harvey 1939-2020 Verfasser (DE-588)115041699 aut Multilevel statistical models Harvey Goldstein 3. ed. London [u.a.] Arnold [u.a.] 2003 XV, 253 graph. Darst. txt rdacontent n rdamedia nc rdacarrier Kendall's library of statistics 3 1. Aufl. u.d.T.: Goldstein, Harvey: Multilevel models in educational and social research Statistisches Modell - Multi-level-Verfahren Mathematisches Modell Sozialwissenschaften Educational tests and measurements Mathematical models Multilevel models (Statistics) Social sciences Mathematical models Social sciences Research Methodology 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 Statistisches Modell (DE-588)4121722-6 gnd rswk-swf Pädagogik (DE-588)4044302-4 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Kontextanalyse (DE-588)4129240-6 gnd rswk-swf 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 Kontextanalyse (DE-588)4129240-6 s Statistisches Modell (DE-588)4121722-6 s 3\p DE-604 4\p DE-604 5\p DE-604 Statistische Analyse (DE-588)4116599-8 s 6\p DE-604 Multivariate Analyse (DE-588)4040708-1 s 7\p DE-604 Kendall's library of statistics 3 (DE-604)BV010165867 3 HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010347230&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 7\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Goldstein, Harvey 1939-2020 Multilevel statistical models Kendall's library of statistics Statistisches Modell - Multi-level-Verfahren Mathematisches Modell Sozialwissenschaften Educational tests and measurements Mathematical models Multilevel models (Statistics) Social sciences Mathematical models Social sciences Research Methodology Sozialwissenschaften (DE-588)4055916-6 gnd Statistische Analyse (DE-588)4116599-8 gnd Multivariate Analyse (DE-588)4040708-1 gnd Statistisches Modell (DE-588)4121722-6 gnd Pädagogik (DE-588)4044302-4 gnd Mathematisches Modell (DE-588)4114528-8 gnd Kontextanalyse (DE-588)4129240-6 gnd |
| subject_GND | (DE-588)4055916-6 (DE-588)4116599-8 (DE-588)4040708-1 (DE-588)4121722-6 (DE-588)4044302-4 (DE-588)4114528-8 (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 | Statistisches Modell - Multi-level-Verfahren Mathematisches Modell Sozialwissenschaften Educational tests and measurements Mathematical models Multilevel models (Statistics) Social sciences Mathematical models Social sciences Research Methodology Sozialwissenschaften (DE-588)4055916-6 gnd Statistische Analyse (DE-588)4116599-8 gnd Multivariate Analyse (DE-588)4040708-1 gnd Statistisches Modell (DE-588)4121722-6 gnd Pädagogik (DE-588)4044302-4 gnd Mathematisches Modell (DE-588)4114528-8 gnd Kontextanalyse (DE-588)4129240-6 gnd |
| topic_facet | Statistisches Modell - Multi-level-Verfahren Mathematisches Modell Sozialwissenschaften Educational tests and measurements Mathematical models Multilevel models (Statistics) Social sciences Mathematical models Social sciences Research Methodology Statistische Analyse Multivariate Analyse Statistisches Modell Pädagogik Kontextanalyse |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010347230&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV010165867 |
| work_keys_str_mv | AT goldsteinharvey multilevelstatisticalmodels |