Unidimensional Item Response Theory Models

Abstract

In Chap. 3, the point will be made that multidimensional item response theory (MIRT) is an outgrowth of both factor analysis and unidimensional item response theory (UIRT). Although this is clearly true, the way that MIRT analysis results are interpreted is much more akin to UIRT. This chapter provides a brief introduction to UIRT with a special emphasis on the components that will be generalized when MIRT models are presented in Chap. 4. This chapter is not a thorough description of UIRT models and their applications. Other texts such as Lord (1980), Hambleton and Swaminathan (1985), Hulin et al. (1983), Fischer and Molenaar (1995), and van der Linden and Hambleton (1997) should be consulted for a more thorough development of UIRT models.

There are two purposes for describing UIRT models in this chapter. The first is to present basic concepts about the modeling of the interaction between persons and test items using simple models that allow a simpler explication of the concepts. The second purpose is to identify shortcomings of the UIRT models that motivated the development of more complex models. As with all scientific models of observed phenomena, the models are only useful to the extent that they provide reasonable approximations to real world relationships. Furthermore, the use of more complex models is only justified when they provide increased accuracy or new insights. One of the purposes of this book is to show that the use of the more complex MIRT models is justified because they meet these criteria.