instruction in this advanced statistical topic.1
1 A thorough and user-friendly guide to IRT in R is offered by Desjardins and Bulut (2018). Also, readers who are less familiar with R should note that many of the models and methods discussed in this volume can be implemented in general statistical software like Mplus (L. Muthén & Muthén, 2017), SAS (SAS Institute Inc., 2015), and SPSS (via the SPIRIT macro; DiTrapani, Rockwood, & Jeon, 2018).
Finally, it is important to note that this book, like many titles in the QASS series, is more of an overview of an advanced statistical method than a technical reference source. In an effort to present MIRT methods and models in a palatable and usable format, the rigorous mathematical underpinnings of MIRT are not discussed herein. If you require derivations and proofs, then you may find a volume such as Baker and Kim (2004) more beneficial.
This book is structured as follows: Chapter 2 offers a brief review of unidimensional IRT (UIRT), covering data assumptions, dichotomous and polytomous UIRT models, descriptive statistics, and UIRT parameter estimation. Each of the sections in Chapter 2 includes only the essential details with limited exposition regarding the finer points of IRT. The goal is to refresh your memory of unidimensional IRT models and methods in preparation for the subsequent chapters on MIRT.
Chapters 3 and 4 expand upon the common UIRT measurement models to include multiple latent traits. Chapter 3 presents MIRT models for dichotomous response data, whereas Chapter 4 focuses on polytomous MIRT models. After describing the testing scenarios in which these models are appropriate, each of these chapters then presents the relevant equations along with numerous visualizations and interpretations of these models and their parameters. Readers should note that this book offers limited information on multidimensional Rasch models. Interested readers may consult Briggs and Wilson (2003) for an introduction to multidimensional Rasch modeling.
Chapter 5 covers several ways of describing the results of a MIRT analysis. One of the many challenges in understanding MIRT models is how to make sense of the parameter estimates and other statistical properties of multidimensional items/tests. This chapter presents both item- and test-level descriptives, including multidimensional item response surfaces, information functions, and other important components of standard MIRT output.
Chapter 6 explores several common MIRT factor structures. These structures describe the overall arrangement of the latent variables, their connections to one another, and their relationships with the item responses. This chapter focuses primarily on a recent development in MIRT modeling: the flexible two-tier item factor analysis model, which encompasses a number of simpler item factor structures, including the popular bifactor model.
Chapter 7 presents several methods of estimating the parameters in the MIRT models discussed in Chapters 3 through 5. This chapter introduces the estimation complications that arise due to the presence of multiple latent traits and then reviews three contemporary techniques of estimating the MIRT model parameters.
Chapter 8 focuses on an important component of any statistical modeling endeavor: the diagnosis and evaluation of the model. This chapter details several MIRT model diagnostics, including dimensionality assessment, test-level goodness of fit, and the evaluation of item-level fit. This chapter will provide you with the tools to carefully appraise the quality of a MIRT model and thereby uncover its strengths and/or shortcomings.
Finally, Chapter 9 presents several informative and cutting-edge applications of MIRT. This chapter presents a handful of the many exciting MIRT applications that have been developed in recent years, including large-scale assessment analysis, longitudinal modeling, linking and equating, differential item functioning, and computerized adaptive testing.
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