Bayesian psychometric modeling:
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| Format: | Buch |
| Sprache: | English |
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Boca Raton ; London ; New York
CRC Press, Taylor & Francis Group
[2016]
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| Schriftenreihe: | Chapman & Hall/CRC statistics in the social and behavioral sciences series
A Chapman & Hall book |
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| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XXVI, 464 Seiten Diagramme |
| ISBN: | 9781439884676 |
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MARC
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| 245 | 1 | 0 | |a Bayesian psychometric modeling |c Roy Levy (Arizona State University Tempe, Arizona, USA), Robert J. Mislevy (Educational Testing Service Princeton New Jersey, USA) |
| 264 | 1 | |a Boca Raton ; London ; New York |b CRC Press, Taylor & Francis Group |c [2016] | |
| 264 | 4 | |c © 2016 | |
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Datensatz im Suchindex
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| adam_text |
Titel: Bayesian psychometric modeling
Autor: Levy, Roy
Jahr: 2016
Contents
Preface.xix
Acknowledgments.xxv
Section I Foundations
1. Overview of Assessment and Psychometric Modeling.3
1.1 Assessment as Evidentiary Reasoning.3
1.2 The Role of Probability.9
1.2.1 Enter Probability.9
1.2.2 Model-Based Reasoning.11
1.2.3 Epistemic Probability.14
1.3 The Role of Context in the Assessment Argument.16
1.4 Evidence-Centered Design.18
1.4.1 Domain Analysis and Domain Modeling.19
1.4.2 Conceptual Assessment Framework.19
1.4.2.1 Student Model.20
1.4.2.2 Task Models.20
1.4.2.3 Evidence Models.21
1.4.3 Assessment Implementation and Assessment Delivery.22
1.4.4 Summary.23
1.5 Summary and Looking Ahead.23
2. Introduction to Bayesian Inference.25
2.1 Review of Frequentist Inference via ML.25
2.2 Bayesian Inference.26
2.3 Bernoulli and Binomial Models.31
2.3.1 Frequentist Modeling for Binomial Distributions
via ML Estimation.31
2.3.2 Bayesian Modeling for Binomial Distributed Data:
The Beta-Binomial Model.32
2.4 Summarizing Posterior Distributions.35
2.5 Graphical Model Representation.36
2.6 Analyses Using WinBUGS.38
2.7 Summary and Bibliographie Note.41
Exercises.43
3. Conceptual Issues in Bayesian Inference.45
3.1 Relative Influence of the Prior Distribution and the Data.45
3.1.1 Effect of the Information in the Prior.45
3.1.2 Effect of the Information in the Data.49
3.1.3 Summary of the Effects of Information in the Prior and the Data.50
3-2 Specifying Prior Distributions.51
3-3 Comparing Bayesian and Frequentist Inferences and Interpretations.53
ix
Contents
3.4 Exchangeability, Conditional Independence, and Bayesian Inference.56
3.4.1 Exchangeability.56
3.4.2 Conditional Independence.58
3.4.3 Exchangeability, Independence, and Random Sampling.59
3.4.4 Conditional Exchangeability.59
3.4.5 Structuring Prior Distributions via Exchangeability.60
3.4.6 Exchangeability, de Finetti's Theorem, Conditional Independence,
and Model Construction.61
3.4.7 Summary of Exchangeability: From Narrative to Structured
Distributions to Parametric Forms.63
3.5 WhyBayes?.65
3.5.1 Epistemic Probability Overlaid with Parameters.65
3.5.2 Prior Probability Judgments Are Always Part of Our Models.66
3.5.3 Exchangeability, de Finetti's Theorem, and Bayesian Modeling.68
3.5.4 Reasoning through the Machinery of the Model.70
3.5.5 Managing and Propagating Uncertainty.70
3.5.6 Incorporating Substantive Knowledge.70
3.5.7 Accumulation of Evidence.71
3.5.8 Conceptual and Computational Simplifications.72
3.5.9 Pragmatics.72
3.6 Conceptualizations of Bayesian Modeling.73
3.7 Summary and Bibliographie Note.74
4. Normal Distribution Models.77
4.1 Model with Unknown Mean and Known Variance.77
4.1.1 Model Setup.77
4.1.2 Normal Prior Distribution.78
4.1.3 Complete Model and Posterior Distribution.78
4.1.4 Precision Parameterization.79
4.1.5 Example Analysis.81
4.1.6 Asymptotics and Connections to Frequentist Approaches.82
4.2 Model with Known Mean and Unknown Variance.82
4.2.1 Model Setup.82
4.2.2 Inverse-Gamma Prior Distribution.83
4.2.3 Complete Model and Posterior Distribution.84
4.2.4 Precision Parameterization and Gamma Prior Distribution.85
4.2.5 Complete Model and Posterior Distribution for the Precision
Parameterization.85
4.2.6 Example Analysis.86
4.3 Model with Unknown Mean and Unknown Variance.87
4.3.1 Model Setup with the Conditionally Conjugate Prior
Distribution.87
4.3.2 Example Analysis.89
4.3.3 Alternative Prior Distributions.90
4.4 Summary. 92
Exercises. 92
Contents xi
5. Markov Chain Monte Carlo Estimation.93
5.1 Overview of MCMC.94
5.2 Gibbs Sampling.96
5.2.1 Gibbs Sampling Algorithm.96
5.2.2 Example: Inference for the Mean and Variance of a Normal
Distribution.97
5.2.3 Discussion.100
5.3 Metropolis Sampling.101
5.4 How MCMC Facilitates Bayesian Modeling.104
5.5 Metropolis-Hastings Sampling.105
5.5.1 Metropolis-Hastings as a Generalization of Metropolis.105
5.5.2 Explaining the Acceptance Probability.105
5.6 Single-Component-Metropolis or Metropolis-within-Gibbs Sampling.107
5.7 Practical Issues in MCMC.107
5.7.1 Implementing a Sampler.108
5.7.2 Assessing Convergence.108
5.7.3 Serial Dependence.110
5.7.4 Mixing.111
5.7.5 Summarizing the Results from MCMC.112
5.8 Summary and Bibliographie Note.112
Exercises.114
6. Regression.117
6.1 Background and Notation.117
6.1.1 Conventional Presentation.117
6.1.2 From a Füll Model of All Observables to a Conditional Model
for the Outcomes.118
6.1.3 Toward the Posterior Distribution.119
6.2 Conditional Probability of the Data.119
6.3 Conditionally Conjugate Prior.120
6.4 Complete Model and Posterior Distribution.121
6.5 MCMC Estimation.122
6.5.1 Gibbs Sampler Routine for Regression.124
6.6 Example: Regressing Test Scores on Previous Test Scores.124
6.6.1 Model Specification.124
6.6.2 Gibbs Sampling.126
6.6.3 MCMC Using WinBUGS.129
6.7 Summary and Bibliographie Note.131
Exercises.131
Section II Psychometrics
7. Canonical Bayesian Psychometric Modeling.135
7.1 Three Kinds of DAGs.135
7.2 Canonical Psychometric Model.136
7.2.1 Running Example: Subtraction Proficiency.139
xü Contents
7.3 Bayesian Analysis.139
7.3.1 Bayesian Analysis for Examinees.139
7.3.1.1 Running Example: Subrraction Prohciency.140
7.3.2 Probability-Model-Based Reasoning in Assessment.141
7.3.3 Enter Measurement Model Parameters.142
7.3.3.1 Running Example: Subtraction Proficiency.143
7.3.4 Füll Bayesian Model.143
7.4 Bayesian Methods and Conventional Psychometric Modeling.144
7.5 Summary and Looking Ahead.148
Exercises.150
8. Classical Test Theory.153
8.1 CTT with Known Measurement Model Parameters and Hyperparameters,
Single Observable (Test or Measure).153
8.1.1 Conventional Model Specification.153
8.1.2 Bayesian Modeling.155
8.1.3 Example.160
8.1.3.1 Analytical Solution.160
8.1.3.2 MCMC Estimation via WinBUGS.162
8.2 CTT with Known Measurement Model Parameters and Hyperparameters,
Multiple Observables (Tests or Measures).164
8.2.1 Conventional Model Specification.164
8.2.2 Bayesian Modeling.165
8.2.2.1 Model Specification.165
8.2.2.2 Hierarchical Specification.166
8.2.2.3 Sufficient Statistics.167
8.2.2.4 Posterior Distribution.167
8.2.3 Example.169
8.2.3.1 Analytical Solution.169
8.2.3.2 MCMC Estimation via WinBUGS.170
8.3 CTT with Unknown Measurement Model Parameters and
Hyperparameters.171
8.3.1 Bayesian Model Specification and Posterior Distribution.171
8.3.2 MCMC Estimation.173
8.3.2.1 Gibbs Sampler Routine for Classical Test Theory.175
8.3.3 Example.176
8.3.3.1 Model Specification and Posterior Distribution.176
8.3.3.2 Gibbs Sampling.177
8.3.3.3 WinBUGS.180
8.4 Summary and Bibliographie Note.181
Exercises.184
9. Confirmatory Factor Analysis.187
9.1 Conventional Factor Analysis.187
9.1.1 Model Specification.187
9.1.2 Indeterminacies in Factor Analysis.190
9.1.3 Model Fitting.190
Contents xiii
9.2 Bayesian Factor Analysis.191
9.2.1 Conditional Distribution of the Observables.192
9.2.1.1 Connecting Distribution-Based and Equation-Based
Expressions.193
9.2.2 Prior Distribution.194
9.2.2.1 Prior Distribution for Latent Variables.194
9.2.2.2 Prior Distribution for Parameters That Govern
the Distribution of the Latent Variables.195
9.2.2.3 Prior Distribution for Measurement Model Parameters.196
9.2.2.4 The Use of a Prior Distribution in ML Estimation.196
9.2.3 Posterior Distribution and Graphical Model.198
9.2.4 MCMC Estimation.198
9.2.4.1 Gibbs Sampler Routine for CFA.201
9.3 Example: Single Latent Variable (Factor) Model.202
9.3.1 DAG Representation.203
9.3.2 Model Specification and Posterior Distribution.204
9.3.3 WinBUGS.205
9.3.4 Results.207
9.4 Example: Multiple Latent Variable (Factor) Model.208
9.4.1 DAG Representation.208
9.4.2 Model Specification and Posterior Distribution.208
9.4.3 WinBUGS.209
9.4.4 Results.212
9.5 CFA Using Summary Level Statistics.212
9.6 Comparing DAGs and Path Diagrams.214
9.7 A Hierarchical Model Construction Perspective.216
9.7.1 Hierarchical Model Based on Exchangeability.216
9.7.2 Hierarchical Modeling under Conditional Exchangeability.217
9.8 Flexible Bayesian Modeling.219
9.9 Latent Variable mdeterminacies from a Bayesian Modeling Perspective.223
9.9.1 lllustrating an Indeterminacy via MCMC.223
9.9.2 Resolving Indeterminacies from a Bayesian
Modeling Perspective.226
9.10 Summary and Bibliographie Note.228
Exercises.229
10. Model Evaluation.231
10.1 Interpretability of the Results.231
10.2 Model Checking.232
10.2.1 The Goal of Model Checking.232
10.2.2 The Logic of Model Checking.233
10.2.3 Residual Analysis.233
10.2.4 Posterior Predictive Model Checking Using Test Statistics.237
10.2.4.1 Example from CFA.238
10.2.5 Posterior Predictive Model Checking Using Discrepancy Measures.240
10.2.5.1 Example from CFA.241
10.2.6 Discussion of Posterior Predictive Model Checking.243
xiv Contents
10.3 Model Comparison.245
10.3.1 Comparison via Comparative Model Criticism.245
10.3.2 Bayes Factor.245
10.3.2.1 Example from CFA.247
10.3.3 Information Criteria.248
10.3.3.1 Example from CFA.249
10.3.4 Predictive Criteria.249
10.3.5 Additional Approaches to Model Comparison.250
Exercises.250
11. Item Response Theory.253
11.1 Conventional IRT Models for Dichotomous Observables.254
11.1.1 Model Specification.254
11.1.2 Indeterminacies.256
11.1.3 Model Fitting.256
11.2 Bayesian Modeling of IRT Models for Dichotomous Observables.257
11.2.1 Conditional Probability of the Observables.257
11.2.2 A Prior Distribution.258
11.2.2.1 Prior Distribution for the Latent Variables.258
11.2.2.2 Normal, Truncated-Normal, and Beta Prior
Distributions for the Measurement Model Parameters.259
11.2.3 Posterior Distribution and Graphical Model.260
11.2.4 MCMC Estimation.261
11.2.4.1 Metropolis-Hastings-within-Gibbs Routine for a3-P
Model for Dichotomous Observables.261
11.2.5 Example: Law School Admissions Test.263
11.2.5.1 Model Specification and Fitting in WinBUGS.264
11.2.5.2 Results.265
11.2.5.3 Model-Data Fit.267
11.2.6 Rationale for Prior for Lower Asymptote.269
11.3 Conventional IRT Models for Polytomous Observables.271
11.4 Bayesian Modeling of IRT Models for Polytomous Observables.272
11.4.1 Conditional Probability of the Observables.272
11.4.2 A Prior Distribution.273
11.4.3 Posterior Distribution and Graphical Model.273
11.4.4 Example: Peer Interaction Items.274
11.4.4.1 Model Specification and Fitting in WinBUGS.275
11.4.4.2 Results.277
11.5 Multidimensional IRT Models.278
11.6 Illustrative Applications.280
11.6.1 Computerized Adaptive Testing.280
11.6.2 Collateral Information about Examinees and Items.282
11.6.3 Plausible Values.283
11.7 Alternative Prior Distributions for Measurement Model Parameters.285
11.7.1 Alternative Univariate Prior Specifications for Models for
Dichotomous Observables.285
11.7.2 Alternative Univariate Prior Specifications for Models for
Polytomous Observables.285
Contents xv
11.7.3 Multivariate Prior Specifications for Dependence among
Parameters.287
11.7.4 A Hierarchical Prior Specification.289
11.8 Latent Response Variable Formulation and Data-Augmented Gibbs
Sampling.292
11.9 Summary and Bibliographie Note.295
Exercises.297
12. Missing Data Modeling.299
12.1 Core Concepts in Missing Data Theory.299
12.2 Inference under Ignorability.301
12.2.1 Likelihood-Based Inference.301
12.2.2 Bayesian Inference.302
12.3 Inference under Nonignorability.306
12.4 Multiple Imputation.307
12.4.1 Imputation Phase.308
12.4.1.1 Obtaining Independent Imputations from MCMC.310
12.4.2 Analysis Phase.311
12.4.3 Pooling Phase.311
12.4.4 Plausible Values Revisited.312
12.5 Latent Variables, Missing Data, Parameters, and Unknowns.312
12.6 Summary and Bibliographie Note.314
Exercises.315
13. Latent Class Analysis.317
13.1 Conventional LCA.318
13.1.1 Model Specification.318
13.1.2 Indeterminacy in LCA.319
13.1.3 Model Fitting.319
13.2 Bayesian LCA.320
13.2.1 Conditional Probability of the Observables.320
13.2.2 Prior Distribution.321
13.2.2.1 Prior Distribution for Latent Variables.321
13.2.2.2 Prior Distribution for Parameters That Govern
the Distribution of the Latent Variables.321
13.2.2.3 Prior Distribution for Measurement Model Parameters.321
13.2.3 Posterior Distribution and Graphical Model.322
13.2.4 MCMC Estimation.323
13.2.4.1 Gibbs Sampling Routine for Polytomous Latent and
Observable Variables.324
13.3 Bayesian Analysis for Dichotomous Latent and Observable Variables.325
13.3.1 Conditional Probability of the Observables.325
13.3.2 Prior Distribution.325
13.3.3 The Complete Model and Posterior Distribution.326
13.3.4 MCMC Estimation.326
13.3.4.1 Gibbs Sampling Routine for Dichotomous Latent and
Observable Variables.327
xvi Contents
13.4 Example: Academic Cheating.328
13.4.1 Complete Model and Posterior Distribution.328
13.4.2 MCMC Estimation.330
13.4.3 WinBUGS.333
13.4.4 Model-Data Fit.337
13.4.5 Model Comparison.338
13.4.6 Comparing the Use of the Füll Posterior with Point Summaries
inScoring.338
13.5 Latent Variable Indeterminacies from a Bayesian Modeling Perspective.339
13.5.1 Illustrating the Indeterminacy.339
13.5.2 Resolving the Indeterminacy.340
13.5.3 The Blurred Line between the Prior and the Likelihood.342
13.6 Summary and Bibliographie Note.342
Exercises.343
14. Bayesian Networks.345
14.1 Overview of BNs.345
14.1.1 Description of BNs.345
14.1.2 BNs as Graphical Models.346
14.1.3 Inference Using BNs.346
14.2 BNs as Psychometric Models.347
14.2.1 Latent Class Models as BNs.347
14.2.2 BNs with Multiple Latent Variables.348
14.3 Fitting BNs.350
14.4 Diagnostic Classification Models.351
14.4.1 Mixed-Number Fraction Subtraction Example.352
14.4.2 Structure of the Distribution for the Latent Variables.353
14.4.3 Structure of the Conditional Distribution for the Observable
Variables.356
14.4.4 Completing the Model Specification.359
14.4.4.1 Prior Distributions for the Parameters That Govern
the Distribution of the Latent Variables.359
14.4.4.2 Prior Distributions for the Parameters That Govern
the Distribution of the Observables.360
14.4.5 The Complete Model and the Posterior Distribution.361
14.4.6 WinBUGS.363
14.4.7 Inferences for Examinees.366
14.4.8 Model-Data Fit.367
14.4.8.1 Checking the Hard Prerequisite Relationship.367
14.4.8.2 Checking Person Fit.370
14.5 BNs in Complex Assessment.372
14.5.1 Structure of the Distribution for the Latent Variables.373
14.5.2 Structure of the Conditional Distribution for the Observable
Variables.378
14.6 Dynamic BNs.383
14.7 Summary and Bibliographie Note.386
Exercises. 339
Contents xvii
15. Conclusion.391
15.1 Bayesas aUseful Framework.391
15.2 Some Caution in Mechanically (or Unthinkingly) Using Bayesian
Approaches.393
15.3 Final Words.395
Appendix A: Füll Conditional Distributions.397
Appendix B: Probability Distributions.417
References.425
Index.453 |
| any_adam_object | 1 |
| author | Levy, Roy Mislevy, Robert J. |
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| id | DE-604.BV043902096 |
| illustrated | Not Illustrated |
| indexdate | 2024-09-20T22:00:10Z |
| institution | BVB |
| isbn | 9781439884676 |
| language | English |
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| physical | XXVI, 464 Seiten Diagramme |
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| record_format | marc |
| series2 | Chapman & Hall/CRC statistics in the social and behavioral sciences series A Chapman & Hall book |
| spelling | Levy, Roy Verfasser (DE-588)1123832587 aut Bayesian psychometric modeling Roy Levy (Arizona State University Tempe, Arizona, USA), Robert J. Mislevy (Educational Testing Service Princeton New Jersey, USA) Boca Raton ; London ; New York CRC Press, Taylor & Francis Group [2016] © 2016 XXVI, 464 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Chapman & Hall/CRC statistics in the social and behavioral sciences series A Chapman & Hall book Bayes-Verfahren (DE-588)4204326-8 gnd rswk-swf Bayes-Verfahren (DE-588)4204326-8 s DE-604 Mislevy, Robert J. Verfasser (DE-588)1126526088 aut Erscheint auch als Online-Ausgabe Levy, Roy Bayesian psychometric modeling 9781439884683 (DE-604)BV045488716 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029311319&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Levy, Roy Mislevy, Robert J. Bayesian psychometric modeling Bayes-Verfahren (DE-588)4204326-8 gnd |
| subject_GND | (DE-588)4204326-8 |
| title | Bayesian psychometric modeling |
| title_auth | Bayesian psychometric modeling |
| title_exact_search | Bayesian psychometric modeling |
| title_full | Bayesian psychometric modeling Roy Levy (Arizona State University Tempe, Arizona, USA), Robert J. Mislevy (Educational Testing Service Princeton New Jersey, USA) |
| title_fullStr | Bayesian psychometric modeling Roy Levy (Arizona State University Tempe, Arizona, USA), Robert J. Mislevy (Educational Testing Service Princeton New Jersey, USA) |
| title_full_unstemmed | Bayesian psychometric modeling Roy Levy (Arizona State University Tempe, Arizona, USA), Robert J. Mislevy (Educational Testing Service Princeton New Jersey, USA) |
| title_short | Bayesian psychometric modeling |
| title_sort | bayesian psychometric modeling |
| topic | Bayes-Verfahren (DE-588)4204326-8 gnd |
| topic_facet | Bayes-Verfahren |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029311319&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT levyroy bayesianpsychometricmodeling AT mislevyrobertj bayesianpsychometricmodeling |