Item Response Theory

ISBN-13: 9781119716686 / Angielski / Twarda / 2021 / 384 str.

R. Darrell Bock; Robert D. Gibbons

Spis treści

Preface xviiAcknowledgments xix1 Foundations 11.1 The Logic of Item Response Theory 31.2 Model-based Data Analysis 41.3 Origins 51.3.1 Psychometric Scaling 61.3.2 Classical Test Theory 91.3.3 Contributions fromStatistics 101.4 The Population Concept in IRT 111.5 Generalizability Theory 142 Selected Mathematical and Statistical Results 212.1 Points, Point Sets, and Set Operations 212.2 Probability 242.3 Sampling 252.4 Joint, Conditional, and Marginal Probability 262.5 Probability Distributions and Densities 282.6 Describing Distributions 322.7 Functions of RandomVariables 342.7.1 Linear Functions 342.7.2 Nonlinear Functions 372.8 Elements ofMatrix Algebra 372.8.1 PartitionedMatrices 412.8.2 The Kronecker Product 422.8.3 Row and ColumnMatrices 432.8.4 Matrix Inversion 432.9 Determinants 452.10 Matrix Differentiation 452.10.1 Scalar Functions of Vector Variables 462.10.2 Vector Functions of a Vector Variable 472.10.3 Scalar Functions of aMatrix Variable 482.10.4 Chain Rule for Scalar Functions of a Matrix Variable 492.10.5 Matrix Functions of aMatrix Variable 492.10.6 Derivatives of a Scalar Function with Respect to a SymmetricMatrix 502.10.7 Second-order Differentiation 522.11 Theory of Estimation 532.11.1 Analysis of Variance 562.11.2 Estimating VarianceComponents 572.12 MaximumLikelihoodEstimation (MLE) 592.12.1 Likelihood Functions 592.12.2 The LikelihoodEquations 602.12.3 Examples of Maximum Likelihood Estimation 602.12.4 SamplingDistribution of the Estimator 622.12.5 The Fisher-scoring Solution of the Likelihood Equations 632.12.6 Properties of the Maximum Likelihood Estimator (MLE) 632.12.7 Constrained Estimation 642.12.8 Admissibility 642.13 Bayes Estimation 652.14 TheMaximumA Posteriori (MAP) Estimator 682.15 Marginal Maximum Likelihood Estimation (MMLE) 692.15.1 TheMarginal Likelihood Equations 702.15.2 Application in the "Normal-Normal" Case 722.15.3 The EMSolution 752.15.4 The Fisher-scoring Solution 752.16 Probit and LogitAnalysis 772.16.1 ProbitAnalysis 772.16.2 LogitAnalysis 792.16.3 Logit-linearAnalysis 802.16.4 Extension of Logit-linear Analysis to Multinomial Data 822.16.4.1 Graded Categories 832.16.4.2 NominalCategories 852.17 SomeResults fromClassical Test Theory 882.17.1 Test Reliability 902.17.2 Estimating Reliability 912.17.2.1 Bayes Estimation of True Scores 962.17.3 When are the Assumptions of Classical Test Theory Reasonable? 973 Unidimensional IRT Models 1013.1 The General IRT Framework 1033.2 Item ResponseModels 1043.2.1 DichotomousCategories 1053.2.1.1 Normal OgiveModel 1053.2.1.2 2-PLModel 1093.2.1.3 3-PLModel 1113.2.1.4 1-PLModel 1133.2.1.5 Illustration 1143.2.2 PolytomousCategories 1153.2.2.1 Graded CategoriesModel 1183.2.2.2 Illustration 1203.2.2.3 The NominalCategoriesModel 1223.2.2.4 Nominal Multiple-Choice Model 1303.2.2.5 Illustration 1323.2.2.6 Partial CreditModel 1353.2.2.7 Generalized Partial Credit Model 1363.2.2.8 Illustration 1363.2.2.9 Rating ScaleModels 1363.2.3 RankingModel 1394 Item Parameter Estimation - Binary Data 1414.1 Estimation of Item Parameters Assuming Known AttributeValues of the Respondents 1424.1.1 Estimation 1434.1.1.1 The 1-parameterModel 1434.1.1.2 The 2-parameterModel 1444.1.1.3 The 3-parameterModel 1454.2 Estimation of Item Parameters Assuming Unknown Attribute Values of the Respondents 1464.2.1 Joint Maximum Likelihood Estimation (JML) 1474.2.1.1 The 1-parameter Logistic Model 1474.2.1.2 Logit-linearAnalysis 1484.2.1.3 Proportional Marginal Adjustments 1534.2.2 Marginal Maximum Likelihood Estimation (MML) 1584.2.2.1 The 2-parameterModel 1625 Item Parameter Estimation - Polytomous Data 1775.1 General Results 1775.2 The Normal OgiveModel 1825.3 The NominalCategoriesModel 1835.4 The Graded CategoriesModel 1855.5 The Generalized Partial Credit Model 1885.5.1 The Unrestricted Version 1895.5.2 The EMSolution 1905.5.2.1 The GPCM Newton-Gauss Joint Solution 1915.5.3 Rating ScaleModels 1915.5.3.1 The EMSolution for the RSM 1925.5.3.2 The Newton-Gauss Solution for the RSM 1935.6 Boundary Problems 1945.7 MultipleGroupModels 1965.8 Discussion 1975.9 Conclusions 2006 Multidimensional IRT Models 2016.1 Classical Multiple Factor Analysis of Test Scores 2026.2 Classical Item Factor Analysis 2036.3 Item Factor Analysis Based on Item Response Theory 2056.4 Maximum Likelihood Estimation of Item Slopes and Intercepts 2066.4.1 Estimating Parameters of the Item Response Model 2086.5 Indeterminacies of Item Factor Analysis 2126.5.1 Direction of Response 2126.5.2 Indeterminacy of Location and Scale 2126.5.3 Rotational Indeterminacy of Factor Loadings in exploratory Factor Analysis 2136.5.3.1 Varimax Factor Pattern 2146.5.3.2 Promax Factor Pattern 2146.5.3.3 General andGroup Factors 2156.5.3.4 Confirmatory Item Factor Analysis and the Bifactor Pattern 2156.6 Estimation of Item Parameters and Respondent Scores in Item Bifactor Analysis 2186.7 Estimating Factor Scores 2196.8 Example 2206.8.1 Exploratory Item Factor Analysis 2216.8.2 Confirmatory Item Bifactor Analysis 2236.9 Two-tierModel 2276.10 Summary 2307 Analysis of Dimensionality 2337.1 Unidimensional Models and Multidimensional Data 2347.2 Limited-InformationGoodness of Fit Tests 2377.3 Example 2407.3.1 Exploratory Item Factor Analysis 2407.3.2 Confirmatory Item Bifactor Analysis 2417.4 Discussion 2428 Computerized Adaptive Testing 2438.1 What is Computerized AdaptiveTesting? 2438.2 Computerized Adaptive Testing - An Overview 2448.3 Item Selection 2458.3.1 UnidimensionalComputerized Adaptive Testing (UCAT) 2468.3.1.1 Fisher Information in IRT Model 2468.3.1.2 Maximizing Fisher Information (MFI) and Its Limitations 2488.3.1.3 Modifications toMFI 2498.3.2 MultidimensionalComputerized Adaptive Testing (MCAT) 2518.3.2.1 Two Conceptualizations of the Information Function in Multidimensional Space 2528.3.2.2 SelectionMethods inMCAT 2538.3.3 Bifactor IRT 2568.4 Terminating an Adaptive Test 2578.5 AdditionalConsiderations 2588.6 An Example fromMental HealthMeasurement 2608.6.1 The CAT-Mental Health 2618.6.2 Discussion 2649 Differential Item Functioning 2679.1 Introduction 2679.2 Types of DIF 2689.3 TheMantel-Haenszel Procedure 2709.4 Lord'sWald Test 2719.5 LagrangeMultiplier Test 2729.6 LogisticRegression 2739.7 Assessing DIF for the BifactorModel 2759.8 Assessing DIF fromCATData 27610 Estimating Respondent Attributes 27910.1 Introduction 27910.2 Ability Estimation 27910.2.1 MaximumLikelihood28010.2.2 BayesMAP 28110.2.3 Bayes EAP 28110.2.4 Ability Estimation for Polytomous data 28210.2.5 Ability Estimation for Multidimensional IRT Models 28310.2.6 Ability Estimation for the Bifactor Model 28410.2.7 Estimation of the Ability Distribution 28410.2.8 Domain Scores 28511 Multiple Group Item Response Models 28711.1 Introduction 28711.2 IRT Estimation when the Grouping Structure is Known: TraditionalMultipleGroupIRT 28811.2.1 Example 29111.3 IRT Estimation when the Grouping Structure is Unknown: Mixtures of Gaussian Components 29211.3.1 TheMixture Distribution 29311.3.2 The LikelihoodComponent 29511.3.3 Algorithm 29611.3.4 Unequal Variances 29711.4 MultivariateProbit Analysis 29711.4.1 TheModel 29911.4.2 Identification 30011.4.3 Estimation 30011.4.4 Tests of Fit 30111.4.5 Illustration 30211.5 Multilevel IRTModels 30611.5.1 The RaschModel 30611.5.2 The Two-parameter LogisticModel 30811.5.3 Estimation 30811.5.4 Illustration 30912 Test and Scale Development and Maintenance 31112.1 Introduction 31112.2 Item Banking 31112.3 Item Calibration 31412.3.1 The OEMMethod 31512.3.2 TheMEMMethod 31512.3.3 Stocking'sMethod A 31512.3.4 Stocking'sMethod B 31612.4 IRT Equating 31812.4.1 Linking, Scale Aligning and Equating 31812.4.2 Experimental Designs for Equating 31912.4.2.1 SingleGroup (SG)Design 31912.4.2.2 Equivalent Groups (EG) Design 31912.4.2.3 Counterbalanced (CB) Design 31912.4.2.4 The Anchor Test or Nonequivalent Groups with Anchor Test (NEAT) Design 31912.5 Harmonization 32012.6 Item Parameter Drift 32212.7 Summary 32313 Some Interesting Applications 32513.1 Introduction 32513.2 Bio-behavioral Synthesis 32513.3 Mental HealthMeasurement 32813.3.1 The CAT-Depression Inventory 32813.3.2 The CAT-Anxiety Scale 33013.3.3 The Measurement of Suicidality and the Prediction of Future Suicidal Attempt 33113.3.4 Clinician and Self-rated Psychosis Measurement 33213.3.5 Substance Use Disorder 33413.3.6 Special Populations and Differential Item Functioning 33513.3.6.1 Perinatal 33513.3.6.2 Emergency Medicine 33613.3.6.3 Latinos Taking Tests in Spanish 33613.3.6.4 Criminal Justice 33813.3.7 Intensive LongitudinalData 33913.4 IRT inMachine Learning 340Bibliography 343Index 361

O autorze

Darrell Bock is Professor Emeritus at the University of Chicago and is one of the world's leading psychometricians. He coined the term Item Response Theory.Robert Gibbons is the Blum-Riese Professor of Biostatistics and Pritzker Scholar at the University of Chicago. He is a Fellow of the American Statistical Association, the Royal Statistical Society, and the International Statistical Institute. He is a pioneer of Multidimensional Item Response Theory.