James Carlson

Introduction to Item Response Theory Models and Applications

• Broschiertes Buch

Produktbeschreibung

This is a highly accessible, comprehensive introduction to item response theory (IRT) models and their use in various aspects of assessment/testing. The book employs a mixture of graphics and simulated data sets to ease the reader into the material and covers the basics required to obtain a solid grounding in IRT.

Written in an easily accessible way that assumes little mathematical knowledge, Carlson presents detailed descriptions of several commonly used IRT models, including those for items scored on a two-point (dichotomous) scale such as correct/incorrect, and those scored on multiple-point (polytomous) scales, such as degrees of correctness. One chapter describes a model in-depth and is followed by a chapter of instructions and illustrations showing how to apply the models to the reader's own work.

This book is an essential text for instructors and higher level undergraduate and postgraduate students of statistics, psychometrics, and measurement theory across the behavioral and social sciences, as well as testing professionals.

Produktdetails

• Multivariate Applications Series
• Verlag: Routledge / Taylor & Francis
• Seitenzahl: 184
• Erscheinungstermin: 13. Oktober 2020
• Englisch
• Abmessung: 254mm x 178mm x 10mm
• Gewicht: 331g
• ISBN-13: 9780367471019
• ISBN-10: 0367471019
• Artikelnr.: 59999762

Autorenporträt

James E. Carlson received his Ph.D. from the University of Alberta, Canada, specializing in applied statistics. He was professor of education at the universities of Pittsburgh, USA, and Ottawa, Canada. He also held psychometric positions at testing organizations and the National Assessment Governing Board, U. S. Department of Education. He is a former editor of the Journal of Educational Measurement and has authored two book chapters and a number of journal articles and research reports.

Inhaltsangabe

1. Introduction



1. Background and Terminology



2. Contents of the Following Chapters






2. Models for Dichotomously-Scored Items






1. Introduction



2. Classical Test theory Models


The Model



Item Parameters and their Estimates

Test Parameters and their Estimates




3. Item Response Theory Models




Introduction

The Normal Ogive Three-Parameter Item Response Theory Model

The Three-Parameter Logistic (3PL) Model

Special Cases: The Two-Parameter and One-Parameter Logistic Models



Relationships Between Probabilities of Alternative Responses



Transformations of Scale

Effects of Changes in Parameters

The Test Characteristic Function

The Item Information Function

The Test Information Function and Standard Errors of Measurement




4. IRT Estimation Methodology




Estimation of Item Parameters

Estimation of Proficiency

Indeterminacy of the Scale in IRT Estimation




5. Summary






3. Analyses of Dichotomously-Scored Item and Test Data






1. Introduction



2. Example Classical Test Theory Analyses with a Small Dataset



3. Test and Item Analyses with a Larger Dataset


CTT Item and Test Analysis Results


4. IRT Item and Test Analysis




IRT Software

Missing Data

Iterative Estimation Methodology

Model Fit




5. IRT Analyses Using PARSCALE


PARSCALE Terminology



Some PARSCALE Options

PARSCALE Item Analysis

PARSCALE Test Analyses




6. IRT Analyses Using flexMIRT




flexMIRT Terminology

Some flexMIRT Options

flexMIRT Item Analyses and Comparisons Between Programs

flexMIRT Test Analyses and Comparisons Between Programs




7. Using IRT Results to Evaluate Items and Tests




Evaluating Estimates of Item Parameters

Evaluating Fit of Models to Items

Evaluating Tests as a Whole or Subsets of Test Items




8. Equating, Linking, and Scaling




Equating

Linking

Scaling

Vertical Scaling




9. Summary






4. Models for Polytomously-Scored Items






1. Introduction



2. The Nature of Polytomously-Scored Items



3. Conditional Probability Forms of Models for Polytomous Items



4. Probability-of-Response Form of the Polytomous Models


The 2PPC Model



The GPC Model

The Graded Response (GR) Model




5. Additional Characteristics of the GPC Model




Effects of Changes in Parameters

Alternative Parameterizations

The Expected Score Function

Functions of Scoring at or Above Categories

Comparison of Conditional Response and P₊ Functions

Item Mapping and Standard Setting

The Test Characteristic Function

The Item Information Function

The Item Category Information Function

The Test Information Function

Conditional Standard Errors of Measurement




6. Summary






5. Analyses of Polytomously-Scored Item and Test Data






1. Generation of Example Data



2. Classical Test Theory Analyses


Item Analyses



Test Analyses




3. IRT Analyses




PARSCALE Item Analyses

flexMIRT Item Analyses and Comparisons with PARSCALE




4. Additional Methods of Using IRT Results to Evaluate Items




Evaluating Estimates of Item Parameters

Evaluating Fit of Models to Item Data

Additional Graphical Methods




5. Test Analyses




PARSCALE Test Analyses

flexMIRT Test Analyses




6. Placing the Results from Different Analyses on the Same Scale



7. Summary






6. Multidimensional Item Response Theory Models






1. Introduction



2. The Multidimensional 3PL Model for Dichotomous Items



3. The Multidimensional 2PL Model for Dichotomous Items



4. Is there a Multidimensional 1PL Model for Dichotomous Items



5. Further Comments on MIRT Models


Alternate Parameterizations



Additional Analyses of MIRT Data




6. Noncompensatory MIRT Models



7. MIRT Models for Polytomous Data



8. Summary






7. Analyses of Multidimensional Item Response Data






1. Response Data Generation



2. MIRT Computer Software



3. MIRT and Factor analyses



4. flexMIRT analyses of Example Generated Data


One-dimensional Solution with Two-Dimensional Data



Two-dimensional Solution




5. Summary






8. Overview of More Complex Item Response Theory Models






1. Some More Complex Unidimensional Models


Multigroup Models



Adaptive Testing



Mixture Models



Hierarchical Rater Models

Testlet Models




2. More General MIRT Models: Some Further Reading




Hierarchical Models




3. Cognitive Diagnostic Models



4. Summary

References

Appendix A. Some Technical Background

1. Slope of the 3PL Curve at the Inflection Point where

2. Simplifying Notation for GPC Expressions

3. Some Characteristics of GPC Model Items

Peaks of Response Curves

Crossing Point of P_k and P_k-1

Crossing Point of P₀ and P₂ for m = 3

Symmetry in the Case of m = 3

Limits of the Expected Score Function

Appendix B. Item Category Information Functions

Appendix C. Item Generating Parameters and Classical and IRT Parameter Estimates

Index

Rezensionen

"Carlson's book is a very clear and well-written introduction to item response theory models that should prove very useful to a wide range of students, instructors, researchers and professionals who want to understand the basics of this useful methodology." -- Lisa L. Harlow, professor of psychology at the University of Rhode Island, USA, and series editor for the Multivariate Applications Series (sponsored by SMEP).

"Carlson's book is a very clear and well-written introduction to item response theory models that should prove very useful to a wide range of students, instructors, researchers and professionals who want to understand the basics of this useful methodology." -- Lisa L. Harlow, professor of psychology at the University of Rhode Island, USA, and series editor for the Multivariate Applications Series (sponsored by SMEP).