Ordinal data modeling:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | German |
| Veröffentlicht: |
New York [u.a.]
Springer
2000
|
| Ausgabe: | Corr. 2. print. |
| Schriftenreihe: | Statistics for social science and public policy
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 249 - 254 |
| Beschreibung: | X, 258 S. graph. Darst. |
| ISBN: | 0387987185 |
Internformat
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Datensatz im Suchindex
| _version_ | 1804128831611600896 |
|---|---|
| adam_text | Titel: Ordinal data modeling
Autor: Johnson, Valen E
Jahr: 2000
Contents
Preface v
1 Review of Classical and Bayesian Inference 1
1.1 Learning about a binomial proportion.............. 1
1.1.1 Sampling: The binomial distribution.......... 3
1.1.2 The likelihood function................. 3
1.1.3 Maximum likelihood estimation............ 4
1.1.4 The sampling distribution of the MLE......... 6
1.1.5 Classical point and interval estimation
for a proportion..................... 6
1.1.6 Bayesian inference................... 7
1.1.7 The prior density.................... 7
1.1.8 Updating one s prior beliefs............... 9
1.1.9 Posterior densities with alternative priors........ 10
1.1.10 Summarizing the posterior density........... 13
1.1.11 Prediction........................ 17
1.2 Inference for a normal mean................... 18
1.2.1 A classical analysis................... 19
1.2.2 Bayesian analysis.................... 21
1.3 Inference about a set of proportions............... 23
1.4 Further reading.......................... 27
1.5 Exercises............................. 28
2 Review of Bayesian Computation 33
2.1 Integrals, integrals, integrals,................... 34
2.2 An example........................... 35
2.3 Non-Simulation-Based Algorithms............... 37
2.3.1 The Multivariate normal approximation........ 37
2.3.2 Grid integration..................... 40
2.3.3 Comments about the two computational methods ... 43
2.4 Direct Simulation........................ 43
2.4.1 Simulating random variables.............. 44
2.4.2 Inference based on simulated samples......... 46
2.4.3 Inference for a binomial proportion........... 46
2.4.4 Accuracy of posterior simulation computations .... 48
2.4.5 Direct simulation for a multiparameter posterior:
The composition method................ 49
2.4.6 Inference for a normal mean.............. 49
2.4.7 Direct simulation for a multiparameter posterior with
independent components................ 49
2.4.8 Smoking example (continued) ............. 50
2.5 Markov Chain Monte Carlo................... 53
2.5.1 Introduction....................... 53
2.5.2 Metropolis-Hastings sampling............. 54
2.5.3 Gibbs sampling..................... 58
2.5.4 Output analysis..................... 62
2.6 A two-stage exchangeable model................ 65
2.7 Further reading.......................... 68
2.8 Appendix: Iterative implementation of
Gauss-Hermite quadrature.................... 68
2.9 Exercises............................. 69
Regression Models for Binary Data 75
3.1 Basic modeling considerations ................. 76
3.1.1 Link functions...................... 77
3.1.2 Grouped data...................... 82
3.2 Estimating binary regression coefficients............ 82
3.2.1 The likelihood function................. 82
3.2.2 Maximum likelihood estimation............ 84
3.2.3 Bayesian estimation and inference........... 85
3.2.4 An example....................... 87
3.3 Latent variable interpretation of binary regression....... 90
3.4 Residual analysis and goodness of fit.............. 92
3.4.1 Case analysis...................... 93
3.4.2 Goodness of fit and model selection.......... 102
3.5 An example........................... 108
3.6 A note on retrospective sampling and logistic regression .... 115
3.7 Further reading.......................... 118
3.8 Appendix: iteratively reweighted least squares......... 118
3.9 Exercises............................. 120
Regression Models for Ordinal Data 126
4.1 Ordinal data via latent variables................. 127
4.1.1 Cumulative probabilities and model interpretation ... 130
4.2 Parameter constraints and prior models............. 131
4.2.1 Noninformative priors.................. 131
4.2.2 Informative priors.................... 132
4.3 Estimation strategies....................... 133
4.3.1 Maximum likelihood estimation............ 133
4.3.2 MCMC sampling.................... 134
4.4 Residual analysis and goodness of fit.............. 137
4.5 Examples............................. 139
4.5.1 Grades in a statistics class................ 139
4.6 Prediction of essay scores from grammar attributes....... 148
4.7 Further reading.......................... 153
4.8 Appendix: iteratively reweighted least squares......... 153
4.9 Exercises............................. 155
Analyzing Data from Multiple Raters 158
5.1 Essay scores from five raters .................. 159
5.2 The multiple rater model .................... 161
5.2.1 The likelihood function................. 161
5.2.2 The prior......................... 163
5.2.3 Analysis of essay scores from five raters
(without regression)................... 166
5.3 Incorporating regression functions into multirater data..... 167
5.3.1 Regression of essay grades obtained from five raters . . 171
5.4 ROC analysis .......................... 174
5.5 Further reading.......................... 180
5.6 Exercises............................. 180
Item Response Modeling 182
6.1 Introduction........................... 182
6.2 Modeling the probability of a correct response......... 183
6.2.1 Latent trait........................ 183
6.2.2 Item response curve................... 184
6.2.3 Item characteristics................... 184
6.3 Modeling test results for a group of examinees......... 188
6.3.1 Data structure...................... 188
6.3.2 Model assumptions................... 188
6.4 Classical estimation of item and ability parameters....... 189
6.5 Bayesian estimation of item parameters............. 191
6.5.1 Prior distributions on latent traits............ 191
6.5.2 Prior distributions on item parameters......... 192
6.5.3 Posterior distributions.................. 193
6.5.4 Describing item response models (probit link)..... 193
6.6 Estimation of model parameters (probit link).......... 194
6.6.1 A Gibbs sampling algorithm.............. 195
6.7 An example........................... 197
6.7.1 Posterior inference ................... 199
6.8 One-parameter (item response) models............. 202
6.8.1 The Rasch model.................... 203
6.8.2 A Bayesian fit of the probit one-parameter model . . . 203
6.9 Three-parameter item response models............. 204
6.10 Model checking......................... 205
6.10.1 Bayesian residuals.................... 205
6.10.2 Example......................... 206
6.11 An exchangeable model..................... 207
6.11.1 Prior belief of exchangeability............. 207
6.11.2 Application of a hierarchical prior model to the
shyness data....................... 209
6.12 Further reading.......................... 211
6.13 Exercises............................. 211
7 Graded Response Models: A Case Study of
Undergraduate Grade Data 215
7.1 Background........................... 217
7.1.1 Previously proposed methods for grade adjustment . . 218
7.2 A Bayesian graded response model............... 220
7.2.1 Achievement indices and grade cutoffs......... 220
7.2.2 Prior distributions.................... 222
7.3 Parameter estimation ...................... 225
7.3.1 Posterior simulation................... 225
7.3.2 Posterior optimization.................. 226
7.4 Applications........................... 226
7.4.1 Larkey and Caulkin data ................ 227
7.4.2 A Class of Duke University undergraduates...... 229
7.5 Alternative models and sensitivity analysis........... 231
7.6 Discussion............................ 235
7.7 Appendix: selected transcripts of
Duke University undergraduates................. 236
Appendix: Software for Ordinal Data Modeling 239
References 249
Index 255
|
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| discipline | Mathematik |
| edition | Corr. 2. print. |
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| isbn | 0387987185 |
| language | German |
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| physical | X, 258 S. graph. Darst. |
| publishDate | 2000 |
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| series2 | Statistics for social science and public policy |
| spelling | Johnson, Valen E. Verfasser aut Ordinal data modeling Valen E. Johnson ; James H. Albert Corr. 2. print. New York [u.a.] Springer 2000 X, 258 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Statistics for social science and public policy Literaturverz. S. 249 - 254 Politische Wissenschaft (DE-588)4076229-4 gnd rswk-swf Statistik (DE-588)4056995-0 gnd rswk-swf Sozialwissenschaften (DE-588)4055916-6 gnd rswk-swf Statistik (DE-588)4056995-0 s Sozialwissenschaften (DE-588)4055916-6 s DE-604 Politische Wissenschaft (DE-588)4076229-4 s Albert, Jim 1953- Verfasser (DE-588)133457834 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009568872&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Johnson, Valen E. Albert, Jim 1953- Ordinal data modeling Politische Wissenschaft (DE-588)4076229-4 gnd Statistik (DE-588)4056995-0 gnd Sozialwissenschaften (DE-588)4055916-6 gnd |
| subject_GND | (DE-588)4076229-4 (DE-588)4056995-0 (DE-588)4055916-6 |
| title | Ordinal data modeling |
| title_auth | Ordinal data modeling |
| title_exact_search | Ordinal data modeling |
| title_full | Ordinal data modeling Valen E. Johnson ; James H. Albert |
| title_fullStr | Ordinal data modeling Valen E. Johnson ; James H. Albert |
| title_full_unstemmed | Ordinal data modeling Valen E. Johnson ; James H. Albert |
| title_short | Ordinal data modeling |
| title_sort | ordinal data modeling |
| topic | Politische Wissenschaft (DE-588)4076229-4 gnd Statistik (DE-588)4056995-0 gnd Sozialwissenschaften (DE-588)4055916-6 gnd |
| topic_facet | Politische Wissenschaft Statistik Sozialwissenschaften |
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