Introduction to Item Response Theory Models and Applications

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...

List of contents

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

Report

"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).

Product details

• Authors: James Carlson, James E Carlson, James E. Carlson
• Publisher: Taylor & Francis Ltd.
• Languages: English
• Product format: Paperback / Softback
• Released: 13.10.2020
• EAN: 9780367471019
• ISBN: 978-0-367-47101-9
• No. of pages: 166
• Series: Multivariate Applications Series
• Subjects: Natural sciences, medicine, IT, technology > Natural sciences (general); Non-fiction book > Psychology, esoterics, spirituality, anthroposophy > Psychology: general, reference works; Social sciences, law, business > Media, communication > Communication science