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The Theory and Practice of Item Response Theory
     

The Theory and Practice of Item Response Theory

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by R. J. de Ayala
 

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ISBN-10: 1593858698

ISBN-13: 9781593858698

Pub. Date: 01/20/2009

Publisher: Guilford Publications, Inc.

Item response theory (IRT) is a latent variable modeling approach used to minimize bias and optimize the measurement power of educational and psychological tests and other psychometric applications.

Designed for researchers, psychometric professionals, and advanced students, this book clearly presents both the "how-to" and the "why" of IRT. It

Overview

Item response theory (IRT) is a latent variable modeling approach used to minimize bias and optimize the measurement power of educational and psychological tests and other psychometric applications.

Designed for researchers, psychometric professionals, and advanced students, this book clearly presents both the "how-to" and the "why" of 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.

Product Details

ISBN-13:
9781593858698
Publisher:
Guilford Publications, Inc.
Publication date:
01/20/2009
Series:
Methodology in the Social Sciences Series
Edition description:
New Edition
Pages:
448
Product dimensions:
7.20(w) x 10.10(h) x 1.10(d)

Table of Contents

Symbols and Acronyms

1. Introduction to Measurement

Measurement

Some Measurement Issues

Item Response Theory

Classical Test Theory

Latent Class Analysis

Summary

2. The One-Parameter Model

Conceptual Development of the Rasch Model

The One-Parameter Model

The One-Parameter Logistic Model and the Rasch Model

Assumptions underlying the Model

An Empirical Data Set: The Mathematics Data Set

Conceptually Estimating an Individual's Location

Some Pragmatic Characteristics of Maximum Likelihood Estimates

The Standard Error of Estimate and Information

An Instrument's Estimation Capacity

Summary

3. Joint Maximum Likelihood Parameter Estimation

Joint Maximum Likelihood Estimation

Indeterminacy of Parameter Estimates

How Large a Calibration Sample?

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

Summary

4. Marginal Maximum Likelihood Parameter Estimation

Marginal Maximum Likelihood Estimation

Estimating an Individual's Location: Expected A Posteriori

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

Metric Transformation and the Total Characteristic Function

Summary

5. The Two-Parameter Model

Conceptual Development of the Two-Parameter Model

Information for the Two-Parameter Model

Conceptual Parameter Estimation for the 2PL Model

How Large a Calibration Sample?

Metric Transformation, 2PL Model

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

Information and Relative Efficiency

Summary

6. The Three-Parameter Model

Conceptual Development of the Three-Parameter Model

Additional Comments about the Pseudo-Guessing Parameter, cj

Conceptual Estimation for the 3PL Model

How Large a Calibration Sample?

Assessing Conditional Independence

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

Assessing Person Fit: Appropriateness Measurement

Information for the Three-Parameter Model

Metric Transformation, 3PL Model

Handling Missing Responses

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

Summary

7. Rasch Models for Ordered Polytomous Data

Conceptual Development of the Partial Credit Model

Conceptual Parameter Estimation of the PC Model

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

The Rating Scale Model

Conceptual Estimation of the RS Model

Example: Application of the RS Model to an Attitudes toward Condom Scale, JMLE

How Large a Calibration Sample?

Information for the PC and RS Models

Metric Transformation, PC and RS Models

Summary

8. Non-Rasch Models for Ordered Polytomous Data

The Generalized Partial Credit Model

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

Conceptual Development of the Graded Response Model

How Large a Calibration Sample?

Example: Application of the GR Model to an Attitudes toward Condom Scale, MMLE

Information for Graded Data

Metric Transformation, GPC and GR Models

Summary

9. Models for Nominal Polytomous Data

Conceptual Development of the Nominal Response Model

How Large a Calibration Sample?

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

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

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

Information for the NR Model

Metric Transformation, NR Model

Conceptual Development of the Multiple-Choice Model

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

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

Summary

10. Models for Multidimensional Data

Conceptual Development of a Multidimensional IRT Model

Multidimensional Item Location and Discrimination

Item Vectors and Vector Graphs

The Multidimensional Three-Parameter Logistic Model

Assumptions of the MIRT Model

Estimation of the M2PL Model

Information for the M2PL Model

Indeterminacy in MIRT

Metric Transformation, M2PL Model

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

Obtaining Person Location Estimates

Summary

11. Linking and Equating

Equating Defined

Equating: Data Collection Phase

Equating: Transformation Phase

Example: Application of the Total Characteristic Function Equating

Summary

12. Differential Item Functioning

Differential Item Functioning and Item Bias

Mantel–Haenszel Chi-Square

The TSW Likelihood Ratio Test

Logistic Regression

Example: DIF Analysis

Summary

Appendix A. Maximum Likelihood Estimation of Person Locations

Estimating an Individual's Location: Empirical Maximum Likelihood Estimation

Estimating an Individual's Location: Newton's Method for MLE

Revisiting Zero Variance Binary Response Patterns

Appendix B. Maximum Likelihood Estimation of Item Locations

Appendix C. The Normal Ogive Models

Conceptual Development of the Normal Ogive Model

The Relationship between IRT Statistics and Traditional Item Analysis Indices

Relationship of the Two-Parameter Normal Ogive and Logistic Models

Extending the Two-Parameter Normal Ogive Model to a Multidimensional Space

Appendix D. Computerized Adaptive Testing

A Brief History

Fixed-Branching Techniques

Variable-Branching Techniques

Advantages of Variable-Branching over Fixed-Branching Methods

IRT-Based Variable-Branching Adaptive Testing Algorithm

Appendix E. Miscellanea

Linear Logistic Test Model (LLTM)

Using Principal Axis for Estimating Item Discrimination

Infinite Item Discrimination Parameter Estimates

Example: NOHARM Unidimensional Calibration

An Approximate Chi-Square Statistic for NOHARM

Mixture Models

Relative Efficiency, Monotonicity, and Information

FORTRAN Formats

Example: Mixed Model Calibration of the Science Test–NR and 2PL Models, MMLE

Example: Mixed Model Calibration of the Science Test–NR and GR Models, MMLE

Odds, Odds Ratios, and Logits

The Person Response Function

Linking: A Temperature Analogy Example

Should DIF Analyses Be Based on Latent Classes?

The Separation and Reliability Indices

Dependency in Traditional Item Statistics and Observed Scores

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