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 7: Estimation in MIRT Models
Estimation in MIRT Models
In Chapter 2, we reviewed the estimation of person and item parameters in the context of UIRT modeling. At the most basic level, estimation in MIRT is conceptually similar to estimation in UIRT: The goal is to identify the most likely item and person parameters given some observed pattern of responses. As you may have guessed, however, parameter estimation in MIRT modeling is a far more arduous task. Indeed, multidimensionality drastically complicates the estimation process, and it is only recently, thanks to numerous advancements in statistical methodology and computing power, that we have been able to efficiently estimate MIRT model parameters. While this is certainly the most complex topic in this book, the intention is to provide a relatively general ...