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Polytomous Item Response Theory Models

Polytomous Item Response Theory Models

August 2005 | 120 pages | SAGE Publications, Inc
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.

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Series Editor's Introduction
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  
Relationship to Other IRT Models  
A Practical Example  
3. Polytomous Rasch Models
Partial Credit Model  
Category Steps  
The Mathematical Model  
Relationship to Other IRT Models  
PCM Summary  
Rating Scale Model  
The Mathematical Model  
Model Parameters  
Sufficient Statistics and Other Considerations  
Expected Values and Response Functions  
Response Functions and Information  
Relationship to Other IRT Models  
PCM Scoring Function Formulation and the NRM  
Generalized Partial Credit Model  
Discrimination and Polytomous Rasch Models  
Summary of Polytomous Rasch Models  
Three Practical Examples  
4. Samejima Models
From Response Process to Specific Model  
The Homogeneous Case: Graded Response Models  
The Mathematical Model  
Information for Polytomous Models  
Relationship to Other IRT Models  
From Homogeneous Class to Heterogeneous Class and Back  
A Common Misconception  
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  
Acronyms and Glossary
About the Authors
Key features
  • A unified treatment of the range of polytomous IRT    
  • Simple descriptions of the main philosophical and practical differences between Rasch and non-Rasch polytomous models              
  • A glossary of terms from disparate parts of the literature, including explanations of instances when different terms are used to describe the same features in different models   

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ISBN: 9780761930686

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