Introduction to Item Response Theory Models and Applications
1st Edition
Published on 13. October 2020
Book
Paperback/Softback
166 pages
978-0-367-47101-9 (ISBN)
Description
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.
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.
Reviews / Votes
"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).More details
Series
Language
English
Place of publication
London
United Kingdom
Publishing group
Taylor & Francis Ltd
Target group
College/higher education
Illustrations
124 s/w Abbildungen, 107 s/w Zeichnungen, 17 s/w Tabellen
17 Tables, black and white; 107 Line drawings, black and white; 124 Illustrations, black and white
Dimensions
Height: 254 mm
Width: 178 mm
Thickness: 10 mm
Weight
358 gr
ISBN-13
978-0-367-47101-9 (9780367471019)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
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Book
10/2020
1st Edition
Routledge
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E-Book
10/2020
1st Edition
Routledge
€88.49
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E-Book
10/2020
1st Edition
Routledge
€88.49
Available for download
Person
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.
Content
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
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