The theory and practice of item response theory / R.J. de Ayala.

Format:

Book

Author/Creator:

De Ayala, R. J. (Rafael Jaime), 1957-

Series:

Methodology in the social sciences

Language:

English

Subjects (All):

Item response theory.

Social sciences--Mathematical models.

Social sciences.

Social sciences--Statistical methods.

Psychometrics.

Physical Description:

xv, 448 pages : illustrations ; 26 cm.

Place of Publication:

New York : Guilford Press, [2009]

Summary:

Designed for Researchers, Psychometric Professionals, and Advanced Students, this book clearly presents both the "how-to" and the "why" of item response theory (IRT). It describes simple and more complex IRT models and shows how they are applied with the help of widely available software packages. Chapters follow a consistent format and build sequentially, taking the reader from model development through the fit analysis and interpretation phases that one would perform in practice. The use of common empirical data sets across the chapters facilitates understanding of the various models and how they relate to one another.

Contents:

1 Introduction to Measurement 1

Measurement 1

Some Measurement Issues 3

Item Response Theory 4

Classical Test Theory 5

Latent Class Analysis 7

Summary 9

2 The One-Parameter Model 11

Conceptual Development of the Rasch Model 11

The One-Parameter Model 16

The One-Parameter Logistic Model and the Rasch Model 19

Assumptions Underlying the Model 20

An Empirical Data Set: The mathematics Data Set 21

Conceptually Estimating an Individual's Location 22

Some Pragmatic Characteristics of Maximum Likelihood Estimates 26

The Standard Error of Estimate and Information 27

An Instrument's Estimation Capacity 31

Summary 34

3 Joint Maximum Likelihood Parameter Estimation 39

Joint Maximum Likelihood Estimation 39

Indeterminacy of Parameter Estimates 41

How Large a Calibration Sample? 42

Example: Application of the Rasch Model to the Mathematics Data, JMLE 43

Summary 64

4 Marginal Maximum Likelihood Parameter Estimation 68

Marginal Maximum Likelihood Estimation 68

Estimating an Individual's Location: Expected A Posteriori 75

Example: Application of the Rasch Model to the Mathematics Data, MMLE 80

Metric Transformation and the Total Characteristic Function 92

Summary 96

5 The Two-Parameter Model 99

Conceptual Development of the Two-Parameter Model 99

Information for the Two-Parameter Model 101

Conceptual Parameter estimation for the 2PL Model 103

How Large a Calibration Sample? 104

Metric Transformation, 2PL Model 106

Example: Application of the 2PL Model to the Mathematics Data, MMLE 107

Fit Assessment: An Alternative Approach for Assessing Invariance 110

Information and Relative Efficiency 114

Summary 118

6 The Three-Parameter Model 123

Conceptual Development of the Three-Parameter Model 123

Additional Comments about the Pseudo-Guessing Parameter, Xj 126

Conceptual Parameter Estimation for the 3PL Model 127

How Large a Calibration Sample? 130

Assessing Conditional Independence 131

Example: Application of the 3PL Model to the Mathematics Data, MMLE 134

Assessing Person Fit: Appropriateness Measurement 142

Information for the Three-Parameter Model 144

Metric Transformation, 3PL Model 147

Handling Missing Responses 148

Issues to Consider in selecting among the 1PL, 2PL, and 3PL Models 152

Summary 154

7 Rasch Models for Ordered Polytomous Data 162

Conceptual Development of the Partial Credit Model 163

Conceptual Parameter Estimation of the PC Model 169

Example: Application of the PC Model to a Reasoning Ability Instrument, MMLE 169

The Rating Scale Model 179

Conceptual Estimation of the RS Model 184

Example: Application of the RS Model to an Attitudes Towards Condoms Scale, JMLE 184

How Large a Calibration Sample? 198

Information for the PC and RS Models 200

Metric Transformation, PC and RS Models 201

Summary 202

8 Non-Rasch Models for Ordered Polytomous Data 209

The Generalized Partial Credit Model 209

Example: Application of the GPC Model to a Reasoning Ability Instrument, MMLE 214

Conceptual Development of the Graded Response Model 217

How Large a Calibration Sample? 223

Example: Application of the GR Model to an Attitudes Towards Condoms Scale, MMLE 224

Information for Graded Data 230

Metric Transformation, GPC and GR Models 233

Summary 234

9 Model for Nominal Polytomous Data 237

Conceptual Development of the Nominal Response Model 238

How Large a Calibration Sample? 246

Example: Application of the NR Model to a Science Test, MMLE 248

Example: Mixed Model Calibration of the Science Test-NR and PC Models, MMLE 251

Example: NR and PC Mixed Model Calibration of the Science Test, Collapsed Options, MMLE 254

Information for the NR Model 259

Metric Transformation, NR Model 261

Conceptual Development of the Multiple-Choice Model 261

Example: Application of the MC Model to a Science Test, MMLE 263

Example: Application of the BS Model to a Science Test, MMLE 269

Summary 272

10 Models for Multidimensional Data 275

Conceptual Development of a Multidimensional IRT Model 275

Multidimensional Item Location and Discrimination 281

Item Vectors and Vector Graphs 285

The Multidimensional Three-Parameter Logistic Model 288

Assumptions of the MIRT Model 288

Estimation of the M2PL Model 289

Information for the M2PL Model 290

Indeterminacy in MIRT 291

Metric Transformation, M2PL Model 294

Example: Application of the M2PL Model, Normal-Ogive Harmonic Analysis Robust Method 296

Obtaining Person Location Estimates 302

Summary 303

11 Linking and Equating 306

Equating Defined 306

Equating: Data Collection Phase 307

Equating: Transformation Phase 309

Example: Application of the Total Characteristic Function Equating Method 316

Summary 318

12 Differential Item Functioning 323

Differential Item Functioning and Item Bias 324

Mantel-Haenszel Chi-Sqyare 327

The TSW Likelihood Ratio Test 330

Logistic Regression 331

Example: DIF Analysis 334

Summary 343.

Notes:

Includes bibliographical references (pages 419-438) and indexes.

ISBN:

9781593858698

1593858698

OCLC:

270230503