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.
Chapter 6: Item Factor Structures
Item Factor Structures
Thus far, we have examined a number of multidimensional item-level models. We turn now to test-level models. It is not uncommon to see the general term MIRT model being used in reference to the full test rather than the individual items. Here, we distinguish between item-level MIRT models (such as the M2PL or MGRM from Chapters 3 and 4) and what we will refer to as item factor structures. These test-level models characterize the overall structure of a test—the number of latent dimensions and their associations with one another and with each item (Bock, Gibbons, & Muraki, 1988)—just as in factor analysis or structural equation modeling. Most of the common item factor structures can be considered in the context of the ...