Introduction to Item Response Theory Models and Applications

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.

• Introduction Background and Terminology Contents of the Following Chapters Models for Dichotomously-Scored Items Introduction Classical Test theory ModelsThe ModelItem Parameters and their EstimatesTest Parameters and their Estimates Item Response Theory ModelsIntroductionThe Normal Ogive Three-Parameter Item Response Theory ModelThe Three-Parameter Logistic (3PL) ModelSpecial Cases: The Two-Parameter and One-Parameter Logistic ModelsRelationships Between Probabilities of Alternative ResponsesTransformations of ScaleEffects of Changes in ParametersThe Test Characteristic FunctionThe Item Information FunctionThe Test Information Function and Standard Errors of Measurement IRT Estimation MethodologyEstimation of Item ParametersEstimation of ProficiencyIndeterminacy 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 DatasetCTT Item and Test Analysis Results IRT Item and Test AnalysisIRT SoftwareMissing DataIterative Estimation MethodologyModel Fit IRT Analyses Using PARSCALEPARSCALE TerminologySome PARSCALE OptionsPARSCALE Item AnalysisPARSCALE Test Analyses IRT Analyses Using flexMIRTflexMIRT TerminologySome flexMIRT OptionsflexMIRT Item Analyses and Comparisons Between ProgramsflexMIRT Test Analyses and Comparisons Between Programs Using IRT Results to Evaluate Items and TestsEvaluating Estimates of Item ParametersEvaluating Fit of Models to ItemsEvaluating Tests as a Whole or Subsets of Test Items Equating, Linking, and ScalingEquatingLinkingScaling 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 ModelsThe 2PPC ModelThe GPC ModelThe Graded Response (GR) Model Additional Characteristics of the GPC ModelEffects of Changes in ParametersAlternative ParameterizationsThe Expected Score FunctionFunctions of Scoring at or Above Categories Comparison of Conditional Response and P+ FunctionsItem Mapping and Standard SettingThe Test Characteristic FunctionThe Item Information FunctionThe Item Category Information FunctionThe Test Information FunctionConditional Standard Errors of Measurement Summary Analyses of Polytomously-Scored Item and Test Data Generation of Example Data Classical Test Theory AnalysesItem AnalysesTest Analyses IRT AnalysesPARSCALE Item AnalysesflexMIRT Item Analyses and Comparisons with PARSCALE Additional Methods of Using IRT Results to Evaluate ItemsEvaluating Estimates of Item ParametersEvaluating Fit of Models to Item DataAdditional Graphical Methods Test AnalysesPARSCALE Test AnalysesflexMIRT 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 ModelsAlternate ParameterizationsAdditional 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 DataOne-dimensional Solution with Two-Dimensional DataTwo-dimensional Solution Summary Overview of More Complex Item Response Theory Models Some More Complex Unidimensional ModelsMultigroup ModelsAdaptive TestingMixture ModelsHierarchical Rater ModelsTestlet Models More General MIRT Models: Some Further ReadingHierarchical Models Cognitive Diagnostic Models Summary ReferencesAppendix A. Some Technical Background 1. Slope of the 3PL Curve at the Inflection Point where 2. Simplifying Notation for GPC Expressions3. Some Characteristics of GPC Model ItemsPeaks of Response CurvesCrossing Point of Pk and Pk-1 Crossing Point of P0 and P2 for m = 3Symmetry in the Case of m = 3Limits of the Expected Score FunctionAppendix B. Item Category Information FunctionsAppendix C. Item Generating Parameters and Classical and IRT Parameter EstimatesIndex

"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).