Item response theory irt is arguably one of the most in. Item response theory aka irt is also sometimes called latent trait theory. It covered basic concepts, comparison to ctt methods, relative efficiency, optimal number of choices per item, flexilevel tests, multistage tests, tailored testing, mastery testing, estimating ability and item parameters, equating, item bias, omitted responses, and estimating true score distributions. Abstract item response theory irt observedscore kernel equating is introduced for the nonequivalent groups with anchor test equating design using either chain equating or poststratification equating. This book provides an introduction to test equating, scaling, and linking, including those concepts and practical issues that are critical for developers and all other testing professionals. By using familiar concepts from classical measurement methods and basic statistics, this book introduces the basics of item response theory irt and explains the application of irt methods to problems in test construction, identification of potentially biased test items, test equating and computerizedadaptive testing. Eignor educational testing service, mail stop 32e, rosedale road, princeton, new jersey 08541, u. The book also includes a thorough discussion of alternative.
The results show that irt observedscore kernel equating offers small standard errors and low equating bias under most settings considered. The chapter also discusses some newly developed equating methods with multidimensional irt mirt frameworks. It provides detailed information about how the procedures are implemented when working with real datasets. Ctt methods include tucker, levine, and equipercentile. An approach to scoring and equating tests with binary. Summary this chapter presents an overview of item response theory irt linking and equating procedures with various illustrative examples. The history, theoretical frameworks of classical test theory, item response theory irt, and the most common irt models used in modern testing are presented.
If you want to read one book on item response theory, from the perspective of psychology or behavioral sciences, this should be it. Irt linking and equating the wiley handbook of psychometric. Click download or read online button to get fundamentals of item response theory book now. Other useful packages include ltm rizopoulos, j stat softw 175. Hicks 1983 compared irt equating with fixed versus estimated. This book develops an intuitive understanding of irt principles through the use of graphical displays and analogies to familiar psychological principles. Item response theory item parameters can be estimated using data from a common item equating design either separately for each form or concurrently across forms. Drawing on the work of internationally acclaimed experts in the field, handbook of item response theory, volume 3. While item response theory may be known primarily for its advances in theoretical modeling of responses to test items, equal progress has. Applications presents applications of item response theory to practical testing problems. More specifically it covers the issue of including covariates within the equating process, the use of different kernels and ways of selecting bandwidths in kernel equating, and the bayesian nonparametric estimation of equating functions. Lords book, applications of item response theory to practical testing problems, presented much of the current irt theory in language easily understood by many practitioners. There are several ways of determining equating a new approach to test score equating using item response theory with fixed c.
Test equating traditionally refers to the statistical process of determining comparable scores on different forms of an exam. Test equating, scaling, and linking methods and practices. The theory and practice of item response theory download. Then you can start reading kindle books on your smartphone, tablet, or computer no kindle device required. Also addressed are norming and test equating, topics not typically covered in traditional psychometrics texts. Item response theory columbia university mailman school of. The 3 best approaches for irt equating assess computerized. Item response theory irt test scores equating methods linear equating method equipercentile equating data collection equating tucker, ledyard r scaled scores raw score statistics score distribution standard deviation correlation percentile. The result is that scores from two different test forms. Appropriateness of irt observed score equating university. Click download or read online button to get the theory and practice of item response theory book now. The book has an excellent balance among the technical, conceptual, and practical aspects of item response theory. Because cparameters are on the probability metric, those remain the same before and after transformation.
The dscoring uses information from item response theory ir. Asymptotic standard errors of irt observedscore equating methods. Abstract in this chapter, the theoretical advantages that have been offered for using item response theory irt in the test equating process are discussed. Parameter estimation techniques, second edition statistics. Then you can start reading kindle books on your smartphone, tablet, or computer. Hambletons classic handbook of modern item response theory, this handbook has been expanded from 28 chapters to 85 chapters in three volumes.
In a highly readable way it presents concepts of irt, without requiring to work through the mathematics. Enter your mobile number or email address below and well send you a link to download the free kindle app. While item response theory may be known primarily for its advances in theoretical modeling of responses to test items, equal progress has been made in its providing. This is the definitive textbook on item response theory and irt applications. A truescore equating method, referred to as the ssmirt truescore equating smt procedure, also is developed. This is a modern test theory as opposed to classical test theory. Such procedures rest on two features of the theory. In fundamentals of item response theory, hambleton, swaminathan, and rogers present an alternative test theory p. In this chapter, different methods of item response theory irt linking and equating will be discussed and illustrated using the snsequate gonzalez, j stat softw 597. Equating, item response theory, multiple forms, scoring, testing. This book describes various item response theory models and furnishes detailed explanations of algorithms that can be used to estimate the item and ability parameters.
Standard errors of item response theory equating linking by response function methods. Examining the impact of drifted polytomous anchor items on. Equatinglinking process of placing scores from different test administrations onto a common scale so that scores can be used interchangeably. Equating adjusts for differences in difficulty between test forms. Dec 15, 2017 drawing on the work of internationally acclaimed experts in the field, handbook of item response theory, volume 3. It can be accomplished using either classical test theory or item response theory. Test equating methods are used with many standardized tests in education and psychology to ensure that scores from multiple test forms can be used interchangeably. Jan 01, 2009 item response theory irt is a latent variable modeling approach used to minimize bias and optimize the measurement power of educational and psychological tests and other psychometric applications. This site is like a library, use search box in the widget to get ebook that you.
The equating method is applicable when the two tests to be equated are administered to different groups along with an anchor test. This comprehensive handbook focuses on the most used polytomous item response theory irt models. Simulated tests were constructed to mimic a real largescale test. Drawing on the work of 75 internationally acclaimed experts in the field, handbook of item response theory, threevolume set presents all major item response models, classical and modern statistical tools used in item response theory irt, and major areas of applications of irt in educational and psychological testing, medical diagnosis of patientreported outcomes, and.
Fundamentals of item response theory sage publications ltd. Introduction and history wainer 1990, item response theory, item calibration and proficiency estimation wainer and mislevy 1990. Using familiar concepts from classical measurement methods and basic statistics, hambleton and colleagues introduce the basics of item response theory irt and explain the application of irt methods to problems in test construction, identification of potentially biased test items, test equating, and computerizedadaptive testing. An approach to scoring and equating tests with binary items. Standard errors of item response theory equatinglinking. Numerical standard errors are shown for an actual equating. Fundamentals of item response theory sage publications inc. In addition to test item scaling, irteq also implements true score equating.
Chapter 8 the new psychometrics item response theory. Irteq can equate test scores on the scale of a test to another test using irt true score equating. Essential topics include measurement and statistical concepts, scaling models, test design and development, reliability, validity, factor analysis, item response theory, and generalizability theory. In recent years, researchers from the education, psychology, and statistics communities have contributed to the rapidly growing statistical and psychometric methodologies used in test equating.
Designed for researchers, psychometric professionals, and advanced students, this book clearly presents both the howto and the why of irt. As a result of a comprehensive survey of the related literature, the author provides nuggets of information about a wide range of rules of thumb and analysis alternatives. Drawing on the work of internationally acclaimed experts in the field, handbook of item response theory, volume one. Simplestructure multidimensional item response theory. This chapter covers issues that include scaling person and item parameters, irt true and observed score equating methods, equating using item pools, and equating. It can be accomplished using either classical test theory or item response theory in item response theory, equating is the process of placing scores from two or more parallel test forms onto a common score scale. As the foreword to the book presents, the popularity of item response theory irt is exemplified by its use by large testing organizations in both the. Fundamentals of item response theory download ebook pdf. You can equate forms with classical test theory ctt or item response theory irt. Irt equating is the best methodology to determine comparibility of. It covered basic concepts, comparison to ctt methods, relative efficiency, optimal number of choices per item, flexilevel tests, multistage tests, tailored testing. One of the practical applications of item response theory irt has been test equating lord, 1977, 1980. This suggestion allowed me to fulfill a longstanding desire to develop an instructional software package dealing with item response theory for the. In item response theory, equating is the process of placing scores from two or more parallel test forms onto a common score scale.
It is not the only modern test theory, but it is the most popular one and is currently an area of active research. Irt procedure the item response theory irt model was. Irt test equating with the r package equateirt user. It surveys contemporary irt models, estimation methods, and computer programs. The purpose of this study was to evaluate the combined effects of reduced equating sample size and shortened anchor test length on item response theory irtbased linking and equating results. Under the theory, test equating reduces to finding a linear transformation for positioning. Using item response theory in test score equating sciencedirect. A new approach to test score equating using item response. Irt provides a foundation for statistical methods that are utilized in contexts such as test development, item analysis, equating, item banking, and computerized adaptive testing. While item response theory may be known primarily for its advances in theoretical modeling of responses to test items.
In addition to statistical procedures, successful equating, scaling, and linking involves many aspects of testing, including procedures to develop tests. Scheuneman 1980 produced a book chapter on lt theory and item bias. The text is clear and complete, and can be used by those who wish to work with item reponse theory in all its gory details, or by those who simply wish to have a better understanding of what the subject is all about. Irt facilitates equatinglinking by assuming item parameters for common items do not change over time. Polytomous irt models are given central coverage since many psychological tests use rating scales. A theoretical and conceptual framework for truescore equating using a simplestructure multidimensional item response theory ssmirt model is developed. The basics of item response theory using r statistics for social and behavioral sciences frank b. A practitioners introduction to equating with primers on classical test theory and item response theory prepared for the technical issues in largescale assessment tilsa state collaborative on assessment and student standards scass of the council of chief state school officers ccsso by. Item response theory irt is a latent variable modeling approach used to minimize bias and optimize the measurement power of educational and psychological tests and other psychometric applications. These models help us understand the interaction between examinees and test questions where the questions have various response categories.
Although demars irt can be considered to be an introductory book and requires almost no mathstats background it covers a variety of topics about item response theory. Ability transformations equating item response theory. The equating function is treated in a multivariate setting and the asymptotic covariance matrices of irt observedscore kernel equating functions are derived. In this chapter, the theoretical advantages that have been offered for using item response theory irt in the test equating process are discussed. Contributions to cat were made in a book, computer adaptive testing. More specifically it covers the issue of including covariates within the equating process, the use of different kernels and ways of selecting bandwidths in kernel equating, and the bayesian nonparametric. The magnitude of the item parameter drift, anchor length, number. It is a theory of testing based on the relationship between individuals performances on a test item and. This suggestion allowed me to fulfill a longstanding desire to develop an instructional software package dealing with item response theory for the thenstateoftheart apple ii and ibm pc computers. It is most widely used in education to calibrate and evaluate items in tests, questionnaires, and other instruments and to score subjects on their abilities, attitudes, or other latent traits.
This chapter presents an overview of item response theory irt linking and equating procedures with various illustrative examples. Standard error of an equating by item response theory. Applying test equating methods using r jorge gonzalez. Kolen 1995 have introduced item response theory irt observed score os equating of numbercorrect nc scores for equating different forms of a test. Sep 05, 20 2pl model ability anchoring applied psychological measurement appropriate assessment category response curves chapter classical test theory cognitive comparisons computed correlations dichotomous dimensions embretson endorsed energetic arousal equating estimating trait level examinees example factor analysis function irt models irt trait levels.
Handbook of polytomous item response theory models. This first volume in a threevolume set covers many model developments that have occurred in item response theory irt during the last 20 years. There are three general approaches to irt equating. A narrative overview of the history, theoretical concepts, test theory, and irt is provided to familiarize the. However, one of the reasons that irt was invented was that equating with ctt was very weak. In psychometrics, item response theory irt also known as latent trait theory, strong true score theory, or modern mental test theory is a paradigm for the design, analysis, and scoring of tests, questionnaires, and similar instruments measuring abilities, attitudes, or other variables. Founded 1947, ets pursues research in statistics and psychometrics, making major contributions to areas such as classical test and item response theory, equating test scores, factor analysis, largescale survey assessment research, and test fairness. Hambleton and colleagues introduce the basics of item response theory irt. Irteq windows application that implements irt scaling. The three volumes are thoroughly edited and crossreferenced, with uniform notation, format, and pedagogical principles across all chapters. The expanded coverage in the second edition also includes methodology for using polytomous item response theory in equating. In this chapter, we describe item response theory irt equating methods under various designs.
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