Introduction to Item Response Theory Models and Applications

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.

Zusatztext "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). Informationen zum Autor 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. Klappentext 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. Zusammenfassung 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. Inhaltsverzeichnis Introduction Background and Terminology Contents of the Following Chapters Models for Dichotomously-Scored Items Introduction Classical Test theory Models The Model Item Parameters and their Estimates Test Parameters and their Estimates 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 IRT Estimation Methodology Estimation of Item Parameters Estimation of Proficiency Indeterminacy of the Scale in IRT Estimation Summary Analyses of Dichotomously-Scored Item and Test Data Introduction Example Classical Test Theory Analyses with a Small Dataset Test and Item Analyses with a Larger Dataset CTT Item and Test Analysis Results IRT Item and Test Analysis IRT S...

Autorentext

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.

Inhalt

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 Mult…