图书简介

Symbols and Acronyms 1. Introduction to Measurement - Measurement - Some Measurement Issues - Item Response Theory - Classical Test Theory - Latent Class Analysis - Summary 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 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, BIGSTEPS - Example: Application of the Rasch Model to the Mathematics Data, JMLE, mixRasch - Validity Evidence - Summary 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, BILOG-MG - Metric Transformation and the Total Characteristic Function - Example: Application of the Rasch Model to the Mathematics Data, MMLE, mirt - Summary 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, BILOG-MG - Fit Assessment: An Alternative Approach for Assessing Invariance - Example: Application of the 2PL Model to the Mathematics Data, MMLE, mirt - Information and Relative Efficiency - Summary 6. The Three-Parameter Model - Conceptual Development of the Three-Parameter Model - Additional Comments about the Pseudo-Guessing Parameter, Xⱼ - Conceptual Parameter Estimation for the 3PL Model - How Large a Calibration Sample? - Assessing Conditional Independence - Example: Application of the 3PL Model to the Mathematics Data, MMLE, BILOG-MG - Fit Assessment: Conditional Independence Assessment - Fit Assessment: Model Comparison - Example: Application of the 3PL Model to the Mathematics Data, MMLE, mirt - 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 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, flexMIRT - Example: Application of the PC Model to a Reasoning Ability Instrument, MMLE, mirt - The Rating Scale Model - Conceptual Parameter Estimation of the RS Model - Example: Application of the RS Model to an Attitudes Towards Condoms Scale, JMLE, BIGSTEPS - Example: Application of the PC Model to an Attitudes Towards Condoms Scale, JMLE, mixRasch - How Large a Calibration Sample? - Information for the PC and RS Models - Metric Transformation, PC and RS Models - Summary 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, flexMIRT - Example: Application of the GPC Model to a Reasoning Ability Instrument, MMLE, mirt - Conceptual Development of the Graded Response Model - How Large a Calibration Sample? - Information for Graded Data - Metric Transformation, GPC and GR Models - Example: Application of the GR Model to an Attitudes Towards Condoms Scale, MMLE, flexMIRT - Example: Application of the GR Model to an Attitudes Towards Condoms Scale, MMLE, mirt - Conceptual Development of the Continuous Response Model - Summary 9. Models for Nominal Polytomous Data - Conceptual Development of the Nominal Response Model - Information for the NR Model - Metric Transformation, NR Model - Conceptual Development of the Multiple-Choice Model - How Large a Calibration Sample? - Example: Application of the NR Model to a General Science Test, MMLE, mirt - Summary 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: Calibration of interpersonal engagement instrument, M2PL Model, sirt.noharam - Obtaining Person Location Estimates - Example: Calibration of interpersonal engagement instrument, M2PL Model, mirt - Example: Calibration of interpersonal engagement instrument, M2PL Model, flexMIRT - Summary 11. Linking and Equating - Equating Defined - Equating: Data Collection Phase - Equating: Transformation Phase - Example: Application of the Total Characteristic Function Equating Method, EQUATE - Example: Application of the Total Characteristic Function Equating Method, SNSequate - Example: Fixed-item and Concurrent Calibration Equating - Summary 12. Differential Item Functioning - Differential Item Functioning and Item Bias - Mantel–Haenszel Chi-Square - The TSW Likelihood Ratio Test - Logistic Regression - Example: DIF Analysis of vocabulary test, SAS CMH - Example: DIF Analysis of vocabulary test, mantelhaen.test and difR - Example: DIF Analysis of vocabulary test, SAS proc logistic - Example: DIF Analysis of vocabulary test, glm and difR - Summary 13. Multilevel IRT Models - Multilevel IRT–Two Levels - Example: Equivalence of the Rasch model and its Multilevel Model Parameterization, proc glimmix - Example: Rasch model estimation, lme4 - Person-Level Predictors for Items - Example: Person-Level Predictors for Items–DIF Analysis, proc glimmix - Example: Person-Level Predictors for Items–DIF Analysis, lme4 - Person-Level Predictors for Respondents - Example: Person-Level Predictors for Respondents–Nutrition Literacy, proc glimmix - Example: Person-Level Predictors for Respondents, lme4 - Item-Level Predictors for Items - Example: Item-Level Predictors for Items - Nutrition Literacy, proc glimmix - Example: Item-Level Predictors for Items - Nutrition Literacy, lme4 - Multilevel IRT–Three Levels - Example: Three-Level Model Analysis - Nutrition Literacy, proc glimmix - Example: Three-level analysis of nutrition literacy data, lme4 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. Linear Logistic Test Model (LLTM) - Example of LLTM Calibration using eRm - Appendix F. Mixture Rasch Model - Latent Class Analysis - Mixture Rasch Model - Example: Application of the mixture Rasch Model to Writing Problem Data, CMLE, WINMIRA - Example: Application of the mixture Rasch Model to Writing Problem Data, CMLE, psychomix Appendix G. Miscellanea - Using Principal Axis for Estimating Item Discrimination - Infinite Item Discrimination Parameter Estimates - Example: NOHARM Unidimensional Calibration - An Approximate Chi-Square Statistic for NOHARM - Relative Efficiency, Monotonicity, and Information - FORTRAN Formats - 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 - Conditional Independence using Q₃ - Standalone NOHARM Calibration of interpersonal engagement instrument, M2PL Model - CFI, GFI, M₂, RMSEA, TLI, and SRMR - An Introduction to Kernel Equating - Correspondence between the Rasch model and a Loglinear model - R Introduction References Author Index Subject Index About the Author  

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