Book Review: An Introduction to the Rasch Model with Examples in R

The Rasch model, one of the most influential psychometric models, has played an important role in language testing over the past decades (Aryadoust et al., 2020). However, some existing tools for the Rasch model, such as Facets (Linacre, 2022a) and Winsteps (Linacre, 2022b), are not open freely to the public (trial version available only) and some of the commercial tools might pose a challenge for novices in that manuals are long and hard to follow (Choi & Asilkalkan, 2019). Additionally, the functions and algorithms underlying the Rasch analyses might remain elusive to language testing practitioners. An Introduction to the Rasch Model with Examples in R, a book by Rudolf Debelak, Carolin Stobl, and Matthew D. Zeigenfuse, comes to the rescue timely. It consists of 12 chapters, which are categorized into 3 parts.

Part I (Chapters 1–4) covers the theory of the Rasch model. Chapter 1 presents an introduction to the Rasch model. It delineates the relationship between the Rasch model and other models based on item response theory (IRT). The Rasch model is a special case of the one-parameter logistic model in which the item discrimination is set to 1 for all items (Desjardins & Bulut, 2018, p. 119).

Chapter 2 deals with important concepts of the Rasch model. It begins by introducing the item response function of Rasch, which models the relationship among ability, difficulty, and discrimination. It covers the alternative representations for the modeling of incorrect responses and arbitrary responses. Aside from these two points, it delineates the properties and assumptions of the Rasch model, including local independence and unidimensionality.

Chapter 3 goes further to the parameter estimation of the Rasch model introduced in Chapter 2. Different approaches to the estimation of model parameters and person parameters are discussed in detail, which is followed by the introduction of item and test information. Chapter 3 ends with suggestions for sample size planning for the Rasch model.

Chapter 4 provides detailed information on the test evaluation. It starts with the introduction of graphical assessments including the person item map, empirical item characteristic curves, and the graphical test. This is followed by the introduction of the invariance tests for item and person, such as the likelihood ratio test, and Wald test, which can assess the fairness validity in that these tests can be used to detect differential item functioning (Berrío et al., 2020). It also discusses important indices for the fitness of tests and statistics. The discussion of separation indices for item and person and the techniques for the model comparisons are provided at the end of Chapter 4.

Part I provides detailed information on the Rasch model, which can help language testing practitioners understand the fundamentals of this model. But in practice, we also need to know how to put these functions and algorithms into practice. With this motivation in mind, Part II (Chapters 5–9) is devoted to the applications of the Rasch model with R.

Chapter 5 is the introduction to the R language. It tells us how to install R packages and RStudio for test analyses. It shows the basic techniques in R, such as loading and importing data, and retrieving information, which are helpful to novices without programming experience.

Chapters 6–9 are the demonstrations of analyzing test data using four useful R packages. Chapter 6 demonstrates the usage of the eRm package, which is a powerful R package for fitting the Rasch model. It begins with an introduction of item parameter estimation with the eRm package, which is followed by different ways to extract information. It also exemplifies how to do test evaluation introduced in Chapter 4. These methods for test evaluation can contribute to the scientific assessment of construct validity in language testing.

Chapter 7 presents the procedure of model selection with the mirt package, which can help select the model that best fits the test data. It also illustrates how to conduct and display item parameter estimates. Methods for the evaluation of goodness-of-fit and ability estimation are covered at the end.

Chapter 8 introduces the application of the Rasch model with the TAM package. It shows how to do parameter estimation with the algorithms mentioned in Chapter 3. This chapter also discusses the evaluation of the fitness of the test and person parameter estimation by the TAM package.

Chapter 9 is dedicated to the introduction of the Bayesian estimation of the Rasch model based on the Stan language, which is a probabilistic programming language adopted in the development of psychometric models for its usefulness and flexibility (Luo & Jiao, 2017). The package used in Chapter 9 is called rstan which is an interface between R and Stan. This chapter elaborates on the steps to create and estimate the Rasch model based on the rstan package. What follows is the summary of R commands of three packages (eRm, mirt, and TAM) for conducting Rasch analyses.

Part III (Chapters 10–12) is the section on advanced topics of other IRT models. Chapter 10 discusses the extensions to the Rasch model, including the linear-logistic test model, the mixed Rasch model, the tree-based Rasch model, and multidimensional IRT models. Chapter 11 focuses on the models for polytomous responses, such as the Partial Credit model, the Rating Scale model, the Graded Response model, and the Sequential model. Chapter 12 introduces other important applications of IRT models, including computerized adaptive testing, test equating, and longitudinal IRT models.

Overall, this book is characterized by three distinct strengths. The first merit is embodied by its intuitive introduction of the theoretical foundations for the Rasch model. The details of the Rasch model, different approaches to parameter estimation, and a series of metrics for test invariance and fitness are introduced in this book intuitively. Language testing practitioners can arrive at a clearer understanding of the theory of the Rasch model and other variants of IRT models step by step.

The second strong point of this book is the provision of detailed hands-on tutorials on the Rasch model using R. Part II of the book exemplifies the applications of the theory introduced in Part I. Readers will find that this book is a perfect combination of theory and practice. The examples provided in this book can be replicated if readers run the code shown in the tutorial. Thus, readers can enhance their understanding in practice.

The third strength of this book lies in its interactive design between readers and the book. The book leaves some questions for readers to check their understanding and gives corresponding answers at the end. The book also explains important mathematical formulas of the Rasch model with detailed examples. This makes the learning curve less steep for those without prior mathematical backgrounds.

Although this book presents an introduction to the Rasch model, some language testing practitioners without sufficient motivation for programming might struggle to run and debug the R codes, especially in Chapter 9. It would be more user-friendly if some Shiny-based IRT packages were incorporated into this book. For example, the irtGUI (Yildiz, 2021) R package is a practical and powerful package that can offer the estimation of a series of IRT models. This package can offer a web-based interactive platform in which language testing practitioners can handle Rasch analyses with just several clicks of the mouse.

Despite this missing part, this book serves as an important supplementary reference to the theory and applications of the Rasch model, which can shed light on the development and validation of a test. The packages introduced in the book (eRm, mirt, TAM, and rstan) are powerful tools for the analyses of test data (Nicklin & Vitta, 2022). On the one hand, these packages can help us evaluate or refine test items or scales. They can also, on the other hand, provide empirical evidence for the validation of a test.

In a nutshell, this book provides interactive guidance on the applications of the Rasch model and the steps of conducting test evaluation and validation based on the open-source R packages. Readers will find the flexibility and versatility of the packages because this book goes into details about their powerful functions. Therefore, it is recommended as an important addition to the reference books for the users of the Rasch model which has been widely adopted in language testing research.