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| Symbols and Acronyms | |
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| Introduction to Measurement | |
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| Measurement | |
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| Some Measurement Issues | |
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| Item Response Theory | |
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| Classical Test Theory | |
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| Latent Class Analysis | |
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| Summary | |
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| The One-Parameter Model | |
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| Conceptual Development of the Rasch Model | |
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| The One-Parameter Model | |
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| The One-Parameter Logistic Model and the Rasch Model | |
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| Assumptions Underlying the Model | |
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| An Empirical Data Set: The mathematics Data Set | |
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| Conceptually Estimating an Individual's Location | |
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| Some Pragmatic Characteristics of Maximum Likelihood Estimates | |
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| The Standard Error of Estimate and Information | |
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| An Instrument's Estimation Capacity | |
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| Summary | |
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| Joint Maximum Likelihood Parameter Estimation | |
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| Joint Maximum Likelihood Estimation | |
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| Indeterminacy of Parameter Estimates | |
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| How Large a Calibration Sample? | |
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| Example: Application of the Rasch Model to the Mathematics Data, JMLE | |
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| Summary | |
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| Marginal Maximum Likelihood Parameter Estimation | |
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| Marginal Maximum Likelihood Estimation | |
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| Estimating an Individual's Location: Expected A Posteriori | |
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| Example: Application of the Rasch Model to the Mathematics Data, MMLE | |
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| Metric Transformation and the Total Characteristic Function | |
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| Summary | |
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| The Two-Parameter Model | |
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| Conceptual Development of the Two-Parameter Model | |
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| Information for the Two-Parameter Model | |
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| Conceptual Parameter estimation for the 2PL Model | |
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| How Large a Calibration Sample? | |
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| Metric Transformation, 2PL Model | |
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| Example: Application of the 2PL Model to the Mathematics Data, MMLE | |
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| Fit Assessment: An Alternative Approach for Assessing Invariance | |
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| Information and Relative Efficiency | |
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| Summary | |
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| The Three-Parameter Model | |
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| Conceptual Development of the Three-Parameter Model | |
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| Additional Comments about the Pseudo-Guessing Parameter, Xj | |
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| Conceptual Parameter Estimation for the 3PL Model | |
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| How Large a Calibration Sample? | |
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| Assessing Conditional Independence | |
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| Example: Application of the 3PL Model to the Mathematics Data, MMLE | |
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| Assessing Person Fit: Appropriateness Measurement | |
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| Information for the Three-Parameter Model | |
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| Metric Transformation, 3PL Model | |
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| Handling Missing Responses | |
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| Issues to Consider in selecting among the 1PL, 2PL, and 3PL Models | |
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| Summary | |
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| Rasch Models for Ordered Polytomous Data | |
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| Conceptual Development of the Partial Credit Model | |
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| Conceptual Parameter Estimation of the PC Model | |
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| Example: Application of the PC Model to a Reasoning Ability Instrument, MMLE | |
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| The Rating Scale Model | |
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| Conceptual Estimation of the RS Model | |
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| Example: Application of the RS Model to an Attitudes Towards Condoms Scale, JMLE | |
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| How Large a Calibration Sample? | |
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| Information for the PC and RS Models | |
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| Metric Transformation, PC and RS Models | |
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| Summary | |
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| Non-Rasch Models for Ordered Polytomous Data | |
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| The Generalized Partial Credit Model | |
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| Example: Application of the GPC Model to a Reasoning Ability Instrument, MMLE | |
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| Conceptual Development of the Graded Response Model | |
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| How Large a Calibration Sample? | |
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| Example: Application of the GR Model to an Attitudes Towards Condoms Scale, MMLE | |
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| Information for Graded Data | |
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| Metric Transformation, GPC and GR Models | |
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| Summary | |
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| Model for Nominal Polytomous Data | |
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| Conceptual Development of the Nominal Response Model | |
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| How Large a Calibration Sample? | |
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| Example: Application of the NR Model to a Science Test, MMLE | |
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| Example: Mixed Model Calibration of the Science Test-NR and PC Models, MMLE | |
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| Example: NR and PC Mixed Model Calibration of the Science Test, Collapsed Options, MMLE | |
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| Information for the NR Model | |
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| Metric Transformation, NR Model | |
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| Conceptual Development of the Multiple-Choice Model | |
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| Example: Application of the MC Model to a Science Test, MMLE | |
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| Example: Application of the BS Model to a Science Test, MMLE | |
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| Summary | |
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| Models for Multidimensional Data | |
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| Conceptual Development of a Multidimensional IRT Model | |
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| Multidimensional Item Location and Discrimination | |
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| Item Vectors and Vector Graphs | |
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| The Multidimensional Three-Parameter Logistic Model | |
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| Assumptions of the MIRT Model | |
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| Estimation of the M2PL Model | |
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| Information for the M2PL Model | |
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| Indeterminacy in MIRT | |
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| Metric Transformation, M2PL Model | |
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| Example: Application of the M2PL Model, Normal-Ogive Harmonic Analysis Robust Method | |
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| Obtaining Person Location Estimates | |
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| Summary | |
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| Linking and Equating | |
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| Equating Defined | |
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| Equating: Data Collection Phase | |
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| Equating: Transformation Phase | |
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| Example: Application of the Total Characteristic Function Equating Method | |
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| Summary | |
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| Differential Item Functioning | |
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| Differential Item Functioning and Item Bias | |
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| Mantel-Haenszel Chi-Sqyare | |
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| The TSW Likelihood Ratio Test | |
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| Logistic Regression | |
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| Example: DIF Analysis | |
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| Summary | |
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| Maximum Likelihood Estimation of Person Locations | |
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| Estimating and Individual's Location: Empirical Maximum Likelihood Estimation | |
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| Estimating and Individual's Location: Newton's Method for MLE | |
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| Revisiting Zero Variance Binary Response Patterns | |
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| Maximum Likelihood Estimation of Item Locations | |
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| The Normal Ogive Models | |
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| Conceptual Development of the Normal Ogive Model | |
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| The Relationship between IRT Statistics and Traditional Item Analysis Indices | |
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| Relationship of the Two-Parameter Normal Ogive and Logistic Model | |
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| Extending the Two-Parameter Normal Ogive Model to a Multidimensional Space | |
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| Computerized Adaptive Testing | |
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| A Brief History | |
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| Fixed-Branching Techniques | |
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| Variable-Branching Techniques | |
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| Advantages of Variable-Branching over Fixed-Branching Methods | |
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| IRT-Based Variable-Branching Adaptive Testing Algorithm | |
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| Miscellanea | |
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| Linear Logistic Test Model (LLTM) | |
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| Using Principal Axis for Estimating Item Discrimination | |
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| Infinite Item Discrimination parameter Estimates | |
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| Example: NOHARM Unidimensional Calibration | |
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| An Approximate Chi-Square Statistic for NOHARM | |
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| Mixture Models | |
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| Relative Efficiency, Monotonicity, and Information | |
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| FORTRAN Formats | |
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| Example: Mixed Model Calibration of the Science Test-NR and 2PL Models, MMLE | |
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| Example: Mixed Model Calibration of the Science Test-NR and GR Models, MMLE | |
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| Odds, Odds Ratios, and Logits | |
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| The Person Response Function | |
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| Linking: A Temperature Analogy Example | |
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| Should DIF Analyses Be Based on Latent Classes? | |
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| The Separation and Reliability Indices | |
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| Dependency in Traditional Item Statistics and Observed Scores | |
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| References | |
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| Author Index | |
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| Subject Index | |
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| About the Author | |