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The Theory and Practice of Item Response Theory

by: de Ayala, R. J.

The Theory and Practice of Item Response Theory

by: de Ayala, R. J.

ISBN 13:
9781593858698
ISBN 10:
1593858698
Edition: 1st
Format: Hardcover
Copyright: 12/30/2008
Publisher: The Guilford Press

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Summary

This book has been replaced by The Theory and Practice of Item Response Theory, Second Edition, ISBN 978-1-4625-4775-3.

Symbols and Acronyms	p. xiii
Introduction to Measurement	p. 1
Measurement	p. 1
Some Measurement Issues	p. 3
Item Response Theory	p. 4
Classical Test Theory	p. 5
Latent Class Analysis	p. 7
Summary	p. 9
The One-Parameter Model	p. 11
Conceptual Development of the Rasch Model	p. 11
The One-Parameter Model	p. 16
The One-Parameter Logistic Model and the Rasch Model	p. 19
Assumptions Underlying the Model	p. 20
An Empirical Data Set: The mathematics Data Set	p. 21
Conceptually Estimating an Individual's Location	p. 22
Some Pragmatic Characteristics of Maximum Likelihood Estimates	p. 26
The Standard Error of Estimate and Information	p. 27
An Instrument's Estimation Capacity	p. 31
Summary	p. 34
Joint Maximum Likelihood Parameter Estimation	p. 39
Joint Maximum Likelihood Estimation	p. 39
Indeterminacy of Parameter Estimates	p. 41
How Large a Calibration Sample?	p. 42
Example: Application of the Rasch Model to the Mathematics Data, JMLE	p. 43
Summary	p. 64
Marginal Maximum Likelihood Parameter Estimation	p. 68
Marginal Maximum Likelihood Estimation	p. 68
Estimating an Individual's Location: Expected A Posteriori	p. 75
Example: Application of the Rasch Model to the Mathematics Data, MMLE	p. 80
Metric Transformation and the Total Characteristic Function	p. 92
Summary	p. 96
The Two-Parameter Model	p. 99
Conceptual Development of the Two-Parameter Model	p. 99
Information for the Two-Parameter Model	p. 101
Conceptual Parameter estimation for the 2PL Model	p. 103
How Large a Calibration Sample?	p. 104
Metric Transformation, 2PL Model	p. 106
Example: Application of the 2PL Model to the Mathematics Data, MMLE	p. 107
Fit Assessment: An Alternative Approach for Assessing Invariance	p. 110
Information and Relative Efficiency	p. 114
Summary	p. 118
The Three-Parameter Model	p. 123
Conceptual Development of the Three-Parameter Model	p. 123
Additional Comments about the Pseudo-Guessing Parameter, Xj	p. 126
Conceptual Parameter Estimation for the 3PL Model	p. 127
How Large a Calibration Sample?	p. 130
Assessing Conditional Independence	p. 131
Example: Application of the 3PL Model to the Mathematics Data, MMLE	p. 134
Assessing Person Fit: Appropriateness Measurement	p. 142
Information for the Three-Parameter Model	p. 144
Metric Transformation, 3PL Model	p. 147
Handling Missing Responses	p. 148
Issues to Consider in selecting among the 1PL, 2PL, and 3PL Models	p. 152
Summary	p. 154
Rasch Models for Ordered Polytomous Data	p. 162
Conceptual Development of the Partial Credit Model	p. 163
Conceptual Parameter Estimation of the PC Model	p. 169
Example: Application of the PC Model to a Reasoning Ability Instrument, MMLE	p. 169
The Rating Scale Model	p. 179
Conceptual Estimation of the RS Model	p. 184
Example: Application of the RS Model to an Attitudes Towards Condoms Scale, JMLE	p. 184
How Large a Calibration Sample?	p. 198
Information for the PC and RS Models	p. 200
Metric Transformation, PC and RS Models	p. 201
Summary	p. 202
Non-Rasch Models for Ordered Polytomous Data	p. 209
The Generalized Partial Credit Model	p. 209
Example: Application of the GPC Model to a Reasoning Ability Instrument, MMLE	p. 214
Conceptual Development of the Graded Response Model	p. 217
How Large a Calibration Sample?	p. 223
Example: Application of the GR Model to an Attitudes Towards Condoms Scale, MMLE	p. 224
Information for Graded Data	p. 230
Metric Transformation, GPC and GR Models	p. 233
Summary	p. 234
Model for Nominal Polytomous Data	p. 237
Conceptual Development of the Nominal Response Model	p. 238
How Large a Calibration Sample?	p. 246
Example: Application of the NR Model to a Science Test, MMLE	p. 248
Example: Mixed Model Calibration of the Science Test-NR and PC Models, MMLE	p. 251
Example: NR and PC Mixed Model Calibration of the Science Test, Collapsed Options, MMLE	p. 254
Information for the NR Model	p. 259
Metric Transformation, NR Model	p. 261
Conceptual Development of the Multiple-Choice Model	p. 261
Example: Application of the MC Model to a Science Test, MMLE	p. 263
Example: Application of the BS Model to a Science Test, MMLE	p. 269
Summary	p. 272
Models for Multidimensional Data	p. 275
Conceptual Development of a Multidimensional IRT Model	p. 275
Multidimensional Item Location and Discrimination	p. 281
Item Vectors and Vector Graphs	p. 285
The Multidimensional Three-Parameter Logistic Model	p. 288
Assumptions of the MIRT Model	p. 288
Estimation of the M2PL Model	p. 289
Information for the M2PL Model	p. 290
Indeterminacy in MIRT	p. 291
Metric Transformation, M2PL Model	p. 294
Example: Application of the M2PL Model, Normal-Ogive Harmonic Analysis Robust Method	p. 296
Obtaining Person Location Estimates	p. 302
Summary	p. 303
Linking and Equating	p. 306
Equating Defined	p. 306
Equating: Data Collection Phase	p. 307
Equating: Transformation Phase	p. 309
Example: Application of the Total Characteristic Function Equating Method	p. 316
Summary	p. 318
Differential Item Functioning	p. 323
Differential Item Functioning and Item Bias	p. 324
Mantel-Haenszel Chi-Sqyare	p. 327
The TSW Likelihood Ratio Test	p. 330
Logistic Regression	p. 331
Example: DIF Analysis	p. 334
Summary	p. 343
Maximum Likelihood Estimation of Person Locations	p. 347
Estimating and Individual's Location: Empirical Maximum Likelihood Estimation	p. 347
Estimating and Individual's Location: Newton's Method for MLE	p. 348
Revisiting Zero Variance Binary Response Patterns	p. 354
Maximum Likelihood Estimation of Item Locations	p. 356
The Normal Ogive Models	p. 360
Conceptual Development of the Normal Ogive Model	p. 360
The Relationship between IRT Statistics and Traditional Item Analysis Indices	p. 365
Relationship of the Two-Parameter Normal Ogive and Logistic Model	p. 368
Extending the Two-Parameter Normal Ogive Model to a Multidimensional Space	p. 370
Computerized Adaptive Testing	p. 373
A Brief History	p. 373
Fixed-Branching Techniques	p. 374
Variable-Branching Techniques	p. 375
Advantages of Variable-Branching over Fixed-Branching Methods	p. 375
IRT-Based Variable-Branching Adaptive Testing Algorithm	p. 376
Miscellanea	p. 382
Linear Logistic Test Model (LLTM)	p. 382
Using Principal Axis for Estimating Item Discrimination	p. 384
Infinite Item Discrimination parameter Estimates	p. 385
Example: NOHARM Unidimensional Calibration	p. 387
An Approximate Chi-Square Statistic for NOHARM	p. 389
Mixture Models	p. 391
Relative Efficiency, Monotonicity, and Information	p. 393
FORTRAN Formats	p. 395
Example: Mixed Model Calibration of the Science Test-NR and 2PL Models, MMLE	p. 396
Example: Mixed Model Calibration of the Science Test-NR and GR Models, MMLE	p. 399
Odds, Odds Ratios, and Logits	p. 399
The Person Response Function	p. 403
Linking: A Temperature Analogy Example	p. 405
Should DIF Analyses Be Based on Latent Classes?	p. 407
The Separation and Reliability Indices	p. 408
Dependency in Traditional Item Statistics and Observed Scores	p. 409
References	p. 419
Author Index	p. 439
Subject Index	p. 444
About the Author	p. 448
Table of Contents provided by Ingram. All Rights Reserved.

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The Theory and Practice of Item Response Theory

The Theory and Practice of Item Response Theory

9781593858698

1593858698

Summary

Author Biography

Table of Contents

Supplemental Materials

Write a Review

Amazon no longer offers textbook rentals. We do!

The Theory and Practice of Item Response Theory

The Theory and Practice of Item Response Theory

9781593858698

1593858698

Summary

Author Biography

Table of Contents

Supplemental Materials

Write a Review

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