Multivariate and Mixture Distribution Rasch Models

Extensions and Applications

  • Matthias von Davier
  • Claus H. Carstensen

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

Table of contents

  1. Front Matter
    Pages I-XVIII
  2. Matthias von Davier, Jürgen Rost, Claus H. Carstensen
    Pages 1-12
  3. Multivariate and Mixture Rasch Models

    1. Front Matter
      Pages 13-13
    2. Robert Mislevy, Chun-Wei Huang
      Pages 15-35
    3. Cees A. W. Glas
      Pages 37-55
    4. Matthias von Davier, Kentaro Yamamoto
      Pages 99-115
  4. Generalized Models—Specific Research Questions

    1. Front Matter
      Pages 117-117
    2. Keith A. Boughton, Kentaro Yamamoto
      Pages 147-156
    3. Claus H. Carstensen, Jürgen Rost
      Pages 157-175
    4. Thorsten Meiser
      Pages 191-199
    5. Shelby J. Haberman
      Pages 201-216
    6. Akihito Kamata, Yuk Fai Cheong
      Pages 217-232
  5. Applications of Multivariate and Mixed Rasch Models

  6. Matthias von Davier, Claus H. Carstensen
    Pages E1-E1
  7. Back Matter
    Pages 357-398
  8. Applications of Multivariate and Mixed Rasch Models

    1. Front Matter
      Pages 233-233

About this book


This volume covers extensions of the Rasch model, one of the most researched and applied models in educational research and social science. This collection contains 22 chapters by some of the most recognized international experts in the field. They cover topics ranging from general model extensions to applications in fields as diverse as cognition, personality, organizational and sports psychology, and health sciences and education.

The Rasch model is designed for categorical data, often collected as examinees' responses to multiple tasks such as cognitive items from psychological tests or from educational assessments. The Rasch model's elegant mathematical form is suitable for extensions that allow for greater flexibility in handling complex samples of examinees and collections of tasks from different domains. In these extensions, the Rasch model is enhanced by additional structural elements that either account for differences between diverse populations or for differences among observed variables.

Research on extending well-known statistical tools like regression, mixture distribution, and hierarchical linear models has led to the adoption of Rasch model features to handle categorical observed variables. We maintain both perspectives in the volume and show how these merged models—Rasch models with a more complex item or population structure—are derived either from the Rasch model or from a structural model, how they are estimated, and where they are applied.

Matthias von Davier is a Senior Research Scientist in the Research & Development Division at Educational Testing Service. He is the author of WINMIRA, a software package for estimating latent class models, mixture distribution Rasch models, and hybrid Rasch models. The software grew out of his work with colleagues at the Methodology Department of the Institute for Science Education (IPN) in Kiel, Germany. Von Davier's current research is concerned with extensions of Rasch models and more general Item Response Theory (IRT) models to multidimensional, diagnostic models and with mixture distribution models, with statistical computation and estimation, and with applications of psychometric models in national and international educational assessments.

Claus H. Carstensen is a junior Professor in the Psychometrics and Methodology Department at the IPN, Carstensen's work is concerned with multidimensional extensions of the Rasch model and applications of these models in intelligence and expertise research and educational assessments. He and Juergen Rost, head of the IPN's Methodology Department at the time, developed MULTIRA, a software package for multidimensional Rasch models. Before his current position, Carstensen was a Research Officer at the Australian Council of Educational Research where his focus was large-scale data analysis using multidimensional extensions of the Rasch model.


Likelihood Rasch Model cognition objectivity rasch

Authors and affiliations

  • Matthias von Davier
    • 1
  • Claus H. Carstensen
    • 2
  1. 1.Educational Testing ServicePrincetonUSA
  2. 2.Leibniz-Institut für die Pädagogik der Naturwissenschaften (IPN)University of Kiel, Institute for Science EducationKielGermany

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