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A Short Guide to Item Response Theory Models

  • Textbook
  • Jul 2025

Overview

Authors:
  1. Gerhard Tutz

    1. Department of Statistics, LMU Munich, Munich, Germany

  • Provides a structured survey of modern Item Response Theory models
  • Shows numerous data examples using R
  • Serves as an introductory guide for students and a reference work for researchers

Part of the book series: Statistics for Social and Behavioral Sciences (SSBS)

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About this book

This book presents foundational concepts, essential principles, and practical applications of Item Response Theory (IRT). It provides a structured survey of diverse models that have been put forth, emphasizing both their differences and commonalities.

The main focus is on modern latent trait theory models which provide measurement tools that clearly separate between person abilities and item parameters. The topics covered include the binary Rasch model, its extensions and alternative binary models, ordinal models and their extensions that account for response styles, the thresholds model, classical test theory, response models for count data, differential item functioning, and explanatory item response models. Tree-based item response models, typically not found in classical IRT textbooks, are also addressed.

Applications of the models are illustrated on several data sets from differing areas, showing how models can be fitted and compared. All examples have been computed using R. Code snippets are provided, and the full R code for most of the examples is available online.

The book is aimed at graduate students, applied statisticians, and researchers working in psychometrics, educators, and anyone curious about modeling strategies that enhance the precision and validity of their measurement tools. It serves as an introductory guide for beginners while also providing a resource for those seeking an overview of the plethora of available IRT models.

Keywords

  • Item Response Theory
  • IRT
  • Latent Trait Theory Models
  • R Code
  • Tree-based Item Response Models
  • Binary Models
  • Binary Rasch Model
  • Ordinal Models
  • Thresholds Model
  • Response Models for Count Data
  • Differential Item Functioning
  • Explanatory Item Response Models
  • Classical Test Theory
  • R Package

Authors and Affiliations

  • Department of Statistics, LMU Munich, Munich, Germany

    Gerhard Tutz

About the author

Gerhard Tutz is Professor Emeritus at the Department of Statistics, LMU Munich, Germany. His research interests include multivariate statistics, item response theory and categorical data analysis.

Accessibility Information

PDF accessibility summary

This PDF has been created in accordance with the PDF/UA-1 standard to enhance accessibility, including screen reader support, described non-text content (images, graphs), bookmarks for easy navigation, keyboard-friendly links and forms and searchable, selectable text. We recognize the importance of accessibility, and we welcome queries about accessibility for any of our products. If you have a question or an access need, please get in touch with us at accessibilitysupport@springernature.com. Please note that a more accessible version of this eBook is available as ePub.

EPUB accessibility summary

This ebook is designed with accessibility in mind, aiming to meet the ePub Accessibility 1.0 AA and WCAG 2.2 Level AA standards. It features a navigable table of contents, structured headings, and alternative text for images, ensuring smooth, intuitive navigation and comprehension. The text is reflowable and resizable, with sufficient contrast. We recognize the importance of accessibility, and we welcome queries about accessibility for any of our products. If you have a question or an access need, please get in touch with us at accessibilitysupport@springernature.com.

Bibliographic Information

  • Book Title: A Short Guide to Item Response Theory Models

  • Authors: Gerhard Tutz

  • Series Title: Statistics for Social and Behavioral Sciences

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2025

  • Hardcover ISBN: 978-3-031-87270-9Due: 09 August 2025

  • Softcover ISBN: 978-3-031-87273-0Due: 09 August 2026

  • eBook ISBN: 978-3-031-87271-6Due: 09 August 2025

  • Series ISSN: 2199-7357

  • Series E-ISSN: 2199-7365

  • Edition Number: 1

  • Number of Pages: XI, 249

  • Number of Illustrations: 60 b/w illustrations, 23 illustrations in colour

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