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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 | |