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The Theory and Practice of Item Response Theory


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Table of Contents

Symbols and Acronyms1. Introduction to MeasurementMeasurementSome Measurement IssuesItem Response TheoryClassical Test TheoryLatent Class AnalysisSummary2. The One-Parameter ModelConceptual Development of the Rasch ModelThe One-Parameter ModelThe One-Parameter Logistic Model and the Rasch ModelAssumptions underlying the ModelAn Empirical Data Set: The Mathematics Data SetConceptually Estimating an Individual's LocationSome Pragmatic Characteristics of Maximum Likelihood EstimatesThe Standard Error of Estimate and InformationAn Instrument's Estimation CapacitySummary3. Joint Maximum Likelihood Parameter EstimationJoint Maximum Likelihood EstimationIndeterminacy of Parameter EstimatesHow Large a Calibration Sample?Example: Application of the Rasch Model to the Mathematics Data, JMLESummary4. Marginal Maximum Likelihood Parameter EstimationMarginal Maximum Likelihood EstimationEstimating an Individual's Location: Expected A PosterioriExample: Application of the Rasch Model to the Mathematics Data, MMLEMetric Transformation and the Total Characteristic FunctionSummary5. The Two-Parameter ModelConceptual Development of the Two-Parameter ModelInformation for the Two-Parameter ModelConceptual Parameter Estimation for the 2PL ModelHow Large a Calibration Sample?Metric Transformation, 2PL ModelExample: Application of the 2PL Model to the Mathematics Data, MMLEInformation and Relative EfficiencySummary6. The Three-Parameter ModelConceptual Development of the Three-Parameter ModelAdditional Comments about the Pseudo-Guessing Parameter, cjConceptual Estimation for the 3PL ModelHow Large a Calibration Sample?Assessing Conditional IndependenceExample: Application of the 3PL Model to the Mathematics Data, MMLEAssessing Person Fit: Appropriateness MeasurementInformation for the Three-Parameter ModelMetric Transformation, 3PL ModelHandling Missing ResponsesIssues to Consider in Selecting among the 1PL, 2PL, and 3PL ModelsSummary7. Rasch Models for Ordered Polytomous DataConceptual Development of the Partial Credit ModelConceptual Parameter Estimation of the PC ModelExample: Application of the PC Model to a Reasoning Ability Instrument, MMLEThe Rating Scale ModelConceptual Estimation of the RS ModelExample: Application of the RS Model to an Attitudes toward Condom Scale, JMLEHow Large a Calibration Sample?Information for the PC and RS ModelsMetric Transformation, PC and RS ModelsSummary8. Non-Rasch Models for Ordered Polytomous DataThe Generalized Partial Credit ModelExample: Application of the GPC Model to a Reasoning Ability Instrument, MMLEConceptual Development of the Graded Response ModelHow Large a Calibration Sample?Example: Application of the GR Model to an Attitudes toward Condom Scale, MMLEInformation for Graded DataMetric Transformation, GPC and GR ModelsSummary9. Models for Nominal Polytomous DataConceptual Development of the Nominal Response ModelHow Large a Calibration Sample?Example: Application of the NR Model to a Science Test, MMLEExample: Mixed Model Calibration of the Science Test-NR and PC Models, MMLEExample: NR and PC Mixed Model Calibration of the Science Test, Collapsed Options, MMLEInformation for the NR ModelMetric Transformation, NR ModelConceptual Development of the Multiple-Choice ModelExample: Application of the MC Model to a Science Test, MMLE

About the Author

R. J. de Ayala, Department of Educational Psychology, University of Nebraska--Lincoln, USA


"This book provides a thorough overview of item response theory methodology, with a nice blend of theoretical psychometrics and practical applications. The coverage is quite complete, including the standard dichotomous and polytomous unidimensional models as well as multidimensional models. The examples are very useful." - Mark D. Reckase, Michigan State University, USA "De Ayala does a masterful job of describing the fundamental theory and the many applications of IRT. I am impressed by the breadth of models he covers and the detail he presents on various estimation methods. Coverage includes the standard Rasch; one-, two-, and three-parameter models; polytomous and multidimensional models; and applications to linking/equating and differential item functioning. This is a well-written book that will be useful for graduate students, researchers, and practicing measurement specialists in education, health, and psychology. The greatest strength of this book is de Ayala's ability to present IRT in an engaging, accessible manner." - Bruno D. Zumbo, University of British Columbia, Canada "The book has an excellent structure that covers widely used IRT models and most of their major applications. The author has done an outstanding job of balancing the mathematical with the conceptual, and each chapter contains examples of applications to real data using commercially available software. The text is liberally supplemented by the kinds of graphic displays that can help neophytes understand the complexities of IRT. An especially useful feature is the up-front glossary of notation and acronyms." - David J. Weiss, University of Minnesota, USA; Editor Emeritus, Applied Psychological Measurement "Offers a good roadmap to the complex array of IRT model parameters, estimation methods, and readily available IRT programs. By juxtaposing algebraic development of IRT models (and model estimation) alongside annotated results and software output from applied examples, this book provides an excellent resource for both intermediate and advanced IRT practitioners. The applied researcher will find this book to be an excellent practical resource with numerous examples that use multiple software packages to analyze the same datasets." - Scott M. Hofer, Oregon State University, USA "The text has an excellent balance among the technical, conceptual, and practical aspects of item response theory. It is comprehensive; provides example scripts and output from a variety of popular item response programs; and uses selected data sets throughout the book, making model and program comparisons possible. I also liked the coverage of commonly asked questions related to model fit, item fit, and appropriate sample sizes, which are often missing in item response theory texts." - Kevin J. Grimm, University of California, Davis, USA "This book is jam-packed with useful information. It includes basic, practical programming examples, with clear explanations of WinSTEPS and BILOG scripts, and step-by-step interpretations of goodness of fit in IRT problems. The author also covers more advanced forms of IRT, including multicategory items, multidimensional latent influences, and advanced multiple-group problems of linking and equating. A tour de force!" - John J. McArdle, Head, University of Southern California, USA

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