An Introduction to the Rasch Model with Examples in R

This book provides a concise introduction to the topic of the Rasch model, which has become relatively well-known since it was used in the PISA study. In addition to a clear presentation of the underlying theory, the book also offers a practical introduction to fitting Rasch models by means of the freely available statistical software R.

An Introduction to the Rasch Model with Examples in R offers a clear, comprehensive introduction to the Rasch model along with practical examples in the free, open-source software R.

It is accessible for readers without a background in psychometrics or statistics, while also providing detailed explanations of the relevant mathematical and statistical concepts for readers who want to gain a deeper understanding. Its worked examples in R demonstrate how to apply the methods to real-world examples and how to interpret the resulting output.

In addition to motivating and presenting the Rasch model, the book covers different methods for parameter estimation and for assessing fit and differential item functioning (DIF). While focusing on the Rasch model, it also addresses a variety of other dichotomous and polytomous Rasch and item response theory (IRT) models, such as two-parameter logistic (2PL) and Partial Credit models, and extensions, including mixture Rasch models and computerized adaptive testing (CAT).

Theory is presented in a self-contained way. All necessary mathematical and statistical background is contained in the chapters and appendices. The book also provides detailed, step-by-step instructions for getting started with R and using the eRm, mirt, TAM and rstan packages for fitting Rasch models.

Autorentext

Rudolf Debelak is a Senior Researcher at the University of Zurich, Switzerland. His research interests include psychometrics, with a focus on item response theory, machine learning, and the mathematical and statistical foundations of psychological research methods. Before working in academia, he was employed in the psychological test industry for several years.

Carolin Strobl is a Professor of Psychological Methods at the University of Zurich, Switzerland. Her research spans psychometrics, statistics and machine learning. She has been teaching introductory and advanced courses on statistics and psychometrics for many years and received the 2018 teaching award from her department's student council.

Matthew Zeigenfuse currently works as a data scientist. He spent many years working in academia, researching and teaching cognitive science, psychometrics and Bayesian statistics in both the US and Switzerland.

Inhalt

1 Introduction 2 The Rasch Model 3 Parameter Estimation 4 Test Evaluation 5 Basic R Usage 6 R Package eRm 7 R Package mirt 8 R Package TAM 9 R Interface to Stan 10 Extensions to the Rasch Model 11 Models for Polytomous Responses 12 Outlook on Special Applications