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 3: MIRT Models for Dichotomous Data
MIRT Models for Dichotomous Data
In Chapter 2, we discussed several UIRT models that are designed to measure an examinee’s location along a single latent trait continuum. MIRT models, as the name indicates, involve multiple latent traits. Let us begin our exploration of MIRT modeling by considering the following example, in which Allan, a second-grade student, is presented with a test item:
Item 1: A cheetah sprinted 1.5 kilometers in the morning and rested until the afternoon. In the evening, the cheetah then took a 500-meter stroll to the watering hole. How far did the cheetah travel in total?
On the surface, this item appears to be a standard mathematics word problem designed to measure Allan’s proficiency in addition. Suppose, however, that the probability of responding ...