The theory and practice of item response theory.

Abstract

Symbols and Acronyms. Part 1. Introduction to Measurement. Measurement. Some Measurement Issues. Item Response Theory. Classical Test Theory. Latent Class Analysis. Summary. Part 2. The One-Parameter Model. Conceptual Development of the Rasch Model. The One-Parameter Model. The One-Parameter Logistic Model and the Rasch Model. Assumptions underlying the Model. An Empirical Data Set: The Mathematics Data Set. Conceptually Estimating an Individual's Location. Some Pragmatic Characteristics of Maximum Likelihood Estimates. The Standard Error of Estimate and Information. An Instrument's Estimation Capacity. Summary. Part 3. Joint Maximum Likelihood Parameter Estimation. Joint Maximum Likelihood Estimation. Indeterminacy of Parameter Estimates. How Large a Calibration Sample? Example: Application of the Rasch Model to the Mathematics Data, JMLE. Summary. Part 4. Marginal Maximum Likelihood Parameter Estimation. Marginal Maximum Likelihood Estimation. Estimating an Individual's Location: Expected A Posteriori. Example: Application of the Rasch Model to the Mathematics Data, MMLE. Metric Transformation and the Total Characteristic Function. Summary. Part 5. The Two-Parameter Model. Conceptual Development of the Two-Parameter Model. Information for the Two-Parameter Model. Conceptual Parameter Estimation for the 2PL Model. How Large a Calibration Sample? Metric Transformation, 2PL Model. Example: Application of the 2PL Model to the Mathematics Data, MMLE. Information and Relative Efficiency. Summary. Part 6. The Three-Parameter Model. Conceptual Development of the Three-Parameter Model. Additional Comments about the Pseudo-Guessing Parameter. Conceptual Estimation for the 3PL Model. How Large a Calibration Sample? Assessing Conditional Independence. Example: Application of the 3PL Model to the Mathematics Data, MMLE. Assessing Person Fit: Appropriateness Measurement. Information for the Three-Parameter Model. Metric Transformation, 3PL Model. Handling Missing Responses. Issues to Consider in Selecting among the 1PL, 2PL, and 3PL Models. Summary. Part 7. Rasch Models for Ordered Polytomous Data. Conceptual Development of the Partial Credit Model. Conceptual Parameter Estimation of the PC Model. Example: Application of the PC Model to a Reasoning Ability Instrument, MMLE. The Rating Scale Model. Conceptual Estimation of the RS Model. Example: Application of the RS Model to an Attitudes toward Condom Scale, JMLE. How Large a Calibration Sample? Information for the PC and RS Models. Metric Transformation, PC and RS Models. Summary. Part 8. Non-Rasch Models for Ordered Polytomous Data. The Generalized Partial Credit Model. Example: Application of the GPC Model to a Reasoning Ability Instrument, MMLE. Conceptual Development of the Graded Response Model. How Large a Calibration Sample? Example: Application of the GR Model to an Attitudes toward Condom Scale, MMLE. Information for Graded Data. Metric Transformation, GPC and GR Models. Summary. Part 9. Models for Nominal Polytomous Data. Conceptual Development of the Nominal Response Model. How Large a Calibration Sample? Example: Application of the NR Model to a Science Test, MMLE. Example: Mixed Model Calibration of the Science Test-NR and PC Models, MMLE. Example: NR and PC Mixed Model Calibration of the Science Test, Collapsed Options, MMLE. Information for the NR Model. Metric Transformation, NR Model. Conceptual Development of the Multiple-Choice Model. Example: Application of the MC Model to a Science Test, MMLE. Example: Application of the BS Model to a Science Test, MMLE. Summary. Part 10. Models for Multidimensional Data. Conceptual Development of a Multidimensional IRT Model. Multidimensional Item Location and Discrimination. Item Vectors and Vector Graphs. The Multidimensional Three-Parameter Logistic Model. Assumptions of the MIRT Model. Estimation of the M2PL Model. Information for the M2PL Model. Indeterminacy in MIRT. Metric Transformation, M2PL Model. Example: Application of the M2PL Model, Normal-Ogive Harmonic Analysis Robust Method. Obtaining Person Location Estimates. Summary. Part 11. Linking and Equating. Equating Defined. Equating: Data Collection Phase. Equating: Transformation Phase. Example: Application of the Total Characteristic Function Equating. Summary. Part 12. Differential Item Functioning. Differential Item Functioning and Item Bias. Mantel-Haenszel Chi-Square. The TSW Likelihood Ratio Test. Logistic Regression. Example: DIF Analysis. Summary. Appendix A: Maximum Likelihood Estimation of Person Locations. Estimating an Individual's Location: Empirical Maximum Likelihood Estimation. Estimating an Individual's Location: Newton's Method for MLE. Revisiting Zero Variance Binary Response Patterns. Appendix B: Maximum Likelihood Estimation of Item Locations. Appendix C: The Normal Ogive Models. Conceptual Development of the Normal Ogive Model. The Relationship between IRT Statistics and Traditional Item Analysis Indices. Relationship of the Two-Parameter Normal Ogive and Logistic Models. Extending the Two-Parameter Normal Ogive Model to a Multidimensional Space. Appendix D: Computerized Adaptive Testing. A Brief History. Fixed-Branching Techniques. Variable-Branching Techniques. Advantages of Variable-Branching over Fixed-Branching Methods. IRT-Based Variable-Branching Adaptive Testing Algorithm. Appendix E. Miscellanea. Linear Logistic Test Model (LLTM). Using Principal Axis for Estimating Item Discrimination. Infinite Item Discrimination Parameter Estimates. Example: NOHARM Unidimensional Calibration. An Approximate Chi-Square Statistic for NOHARM. Mixture Models. Relative Efficiency, Monotonicity, and Information. FORTRAN Formats. Example: Mixed Model Calibration of the Science Test-NR and 2PL Models, MMLE. Example: Mixed Model Calibration of the Science Test-NR and GR Models, MMLE. Odds, Odds Ratios, and Logits. The Person Response Function. Linking: A Temperature Analogy Example. Should DIF Analyses Be Based on Latent Classes? The Separation and Reliability Indices. Dependency in Traditional Item Statistics and Observed Scores.