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 1: Introduction
In any statistical modeling scenario, whether the model represents atoms or galaxies or the human brain, it is essential that all variables are measured with optimal precision. Without exact and meticulous measurement, the model may not be an accurate representation of the real-world phenomena under investigation. In the field of psychometrics, the variables in the model are psychological in nature—academic proficiency, personality traits, severity of psychiatric symptoms, and so on. Psychological constructs such as these are inherently complicated and multifaceted, and relatively simple models that only measure a single construct are often insufficient approximations of complex data. As Zhang (2007) noted, “the unidimensionality of a set of items usually cannot be met and most tests are actually multidimensional to some extent” (p. 69). ...