Explanatory Item Response Models: A Brief Introduction

In this chapter we illustrate the use of item response models to analyze data resulting from the measurement of competencies. These item response models deal with data from an instrument such as a test, an inventory, an attitude scale, or a questionnaire – we will call this “test data”. The main purpose of using item response models is the measurement of propensities: specifically, abilities, skills, achievement levels, traits, attitudes, etc. In standard item response modeling each item is modeled with its own set of parameters and in one way or another, the person parameters are also estimated – we will call this the “measurement” approach. In a broader approach, which does not contradict but complements the measurement approach, one might want to model how the properties of the items and the persons making the responses lead to the persons’ responses – we will call this the “explanatory” approach (De Boeck & Wilson, 2004). Understanding how the item responses are generated implies that the responses can be explained in terms of properties of items and of persons. We also take a broader statistical approach than that of standard item response models. It turns out that most extant item response models are special cases of what are called generalized linear or nonlinear mixed models (GLMMs and NLMMs; McCulloch & Searle, 2001). In this chapter, the perspective that is taken on these models is quite simple in its general expression (although it is not necessarily simple in how it is applied to a specific situation) and it has several advantages. We see it as being straightforward because the similarities and differences between models can be described in terms of the kinds of predictors (item properties, person properties, and interactions of item and person properties) and the kinds of weights they have, just as in the familiar regression model. Perhaps the most important feature of the broader approach is that it facilitates the implementation of the explanatory perspective described above. Additional important advantages we see are that the approach is general and therefore also flexible, and it connects psychometrics strongly to the field of statistics, so that a broader knowledge base and more literature become available. One can also see this chapter as dealing primarily with repeated observations which