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.

MIRT Models for Polytomous Data

MIRT models are also capable of accommodating items that are measured on a polytomous scale. Consider another example, in which Fumiko, a ninth-grade student, is presented with a psychological test item:

Item 2: I enjoy social situations.

  • Always
  • Sometimes
  • Never

The item is polytomous because Fumiko is presented with multiple response options. Suppose that a clinical psychologist has hypothesized that a response of Never to Item 2 reflects a relatively high degree of anxiety (θanx) and/or introversion (θint). The probability of Fumiko’s response to this 2-dimensional polytomous item could be modeled using a number of (compensatory1) polytomous MIRT models. We discuss three such models in this chapter.

The multidimensional graded response model. Recall from Chapter 2 that the GRM is a difference model: The boundaries ...

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