Polytomous Item Response Theory Models

Polytomous Item Response Theory Models provides a unified, comprehensive introduction to the range of polytomous models available within item response theory (IRT). It begins by outlining the primary structural distinction between the two major types of polytomous IRT models. This focuses on the two types of response probability that are unique to polytomous models and their associated response functions, which are modeled differently by the different types of IRT model. It describes, both conceptually and mathematically, the major specific polytomous models, including the Nominal Response Model, the Partial Credit Model, the Rating Scale model, and the Graded Response Model. Important variations, such as the Generalized Partial Credit Model are also described as are less common variations, such as the Rating Scale version of the Graded Response Model. Relationships among the models are also investigated and the operation of measurement information is described for each major model. Practical examples of major models using real data are provided, as is a chapter on choosing an appropriate model. Figures are used throughout to illustrate important elements as they are described.

Table of Contents:
Series Editor′s Introduction Acknowledgments 1. Introduction Measurement Theory Item Response Theory Applying the IRT Model Reasons for Using Polytomous IRT Models Polytomous IRT Models Two Types of Probabilities Two Types of Polytomous Models Category Boundaries Item Category Response Functions 2. Nominal Response Model The Mathematical Model Information Relationship to Other IRT Models Variations A Practical Example 3. Polytomous Rasch Models Partial Credit Model Category Steps The Mathematical Model Information Relationship to Other IRT Models Variations PCM Summary Rating Scale Model The Mathematical Model Model Parameters Sufficient Statistics and Other Considerations Information Expected Values and Response Functions Response Functions and Information Relationship to Other IRT Models PCM Scoring Function Formulation and the NRM Variations Generalized Partial Credit Model Discrimination and Polytomous Rasch Models Summary of Polytomous Rasch Models Three Practical Examples 4. Samejima Models Framework From Response Process to Specific Model The Homogeneous Case: Graded Response Models The Mathematical Model Information Information for Polytomous Models Relationship to Other IRT Models From Homogeneous Class to Heterogeneous Class and Back A Common Misconception Variations Summary of Samejima Models Potential Weaknesses of the Cumulative Boundary Approach Possible Strengths of the Cumulative Boundary Approach A Practical Example 5. Model Selection General Criteria Mathematical Approaches Fit Statistic Problems An Example Differences in Modeled Outcome Conclusion Acronyms and Glossary Notes References Index About the Authors