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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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