Several decades of psychometric research have led to the development of sophisticated models for multidimensional test data, and in recent years, multidimensional item response theory (MIRT) has become a burgeoning topic in psychological and educational measurement. Considered a cutting-edge statistical technique, the methodology underlying MIRT can be complex, and therefore doesn’t receive much attention in introductory IRT courses. However author Wes Bonifay shows how MIRT can be understood and applied by anyone with a firm grounding in unidimensional IRT modeling. His volume includes practical examples and illustrations, along with numerous figures and diagrams. Multidimensional Item Response Theory includes snippets of R code interspersed throughout the text (with the complete R code included on an accompanying website) to guide readers in exploring MIRT models, estimating the model parameters, generating plots, and implementing the various procedures and applications discussed throughout the book.

Descriptive MIRT Statistics

There are a number of interesting and informative ways to describe the results of a MIRT analysis. This chapter presents several descriptive MIRT statistics, including multidimensional difficulty and discrimination parameters, conditional probabilities, information functions, and predicted item scores, among other descriptives. We focus mostly on the compensatory M2PL model, though most of the descriptive statistics and interpretations that we explore can be directly extended to the more complex dichotomous and polytomous MIRT models presented in the previous chapters. We begin our discussion by detailing three descriptive statistics that are essential to comprehending MIRT modeling: the θ-space, the multidimensional discrimination index, and the multidimensional difficulty index.

The θ-Space

The θ scale in UIRT, while technically unbounded, is often considered within a reasonable range, such ...

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