Introduction to Item Response Theory Models and Applications

 
 
Routledge (Verlag)
  • 1. Auflage
  • |
  • erscheint ca. am 13. Oktober 2020
  • |
  • 192 Seiten
 
E-Book | ePUB ohne DRM | Systemvoraussetzungen
978-1-000-19538-5 (ISBN)
 

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.

1. Auflage
  • Englisch
  • London
  • |
  • Großbritannien
Taylor & Francis Ltd
  • Für höhere Schule und Studium
124 schwarz-weiße Abbildungen, 107 schwarz-weiße Zeichnungen, 17 schwarz-weiße Tabellen
  • 16,49 MB
978-1-000-19538-5 (9781000195385)
weitere Ausgaben werden ermittelt

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.

  1. 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 Software

        Missing Data

        Iterative Estimation Methodology

        Model Fit

        • IRT Analyses Using PARSCALE

        PARSCALE Terminology

        Some PARSCALE Options

        PARSCALE Item Analysis

        PARSCALE Test Analyses

        • IRT Analyses Using flexMIRT

        flexMIRT Terminology

        Some flexMIRT Options

        flexMIRT Item Analyses and Comparisons Between Programs

        flexMIRT Test Analyses and Comparisons Between Programs

        • 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

        • Equating, Linking, and Scaling

        Equating

        Linking

        Scaling

        Vertical Scaling

        • Summary

        • Models for Polytomously-Scored Items

          • Introduction

          • The Nature of Polytomously-Scored Items

          • Conditional Probability Forms of Models for Polytomous Items

          • Probability-of-Response Form of the Polytomous Models

          The 2PPC Model

          The GPC Model

          The Graded Response (GR) Model

          • 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

          • Summary

          • Analyses of Polytomously-Scored Item and Test Data

            • Generation of Example Data

            • Classical Test Theory Analyses

            Item Analyses

            Test Analyses

            • IRT Analyses

            PARSCALE Item Analyses

            flexMIRT Item Analyses and Comparisons with PARSCALE

            • Additional Methods of Using IRT Results to Evaluate Items

            Evaluating Estimates of Item Parameters

            Evaluating Fit of Models to Item Data

            Additional Graphical Methods

            • Test Analyses

            PARSCALE Test Analyses

            flexMIRT Test Analyses

            • Placing the Results from Different Analyses on the Same Scale

            • Summary

            • Multidimensional Item Response Theory Models

              • Introduction

              • The Multidimensional 3PL Model for Dichotomous Items

              • The Multidimensional 2PL Model for Dichotomous Items

              • Is there a Multidimensional 1PL Model for Dichotomous Items

              • Further Comments on MIRT Models

              Alternate Parameterizations

              Additional Analyses of MIRT Data

              • Noncompensatory MIRT Models

              • MIRT Models for Polytomous Data

              • Summary

              • Analyses of Multidimensional Item Response Data

                • Response Data Generation

                • MIRT Computer Software

                • MIRT and Factor analyses

                • flexMIRT analyses of Example Generated Data

                One-dimensional Solution with Two-Dimensional Data

                Two-dimensional Solution

                • Summary

                • Overview of More Complex Item Response Theory Models

                  • Some More Complex Unidimensional Models

                  Multigroup Models

                  Adaptive Testing

                  Mixture Models

                  Hierarchical Rater Models

                  Testlet Models

                  • More General MIRT Models: Some Further Reading

                  Hierarchical Models

                  • Cognitive Diagnostic Models

                  • 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 Pk and Pk-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

                  "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).

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