Chapter 5 Abstract

 

            The aim of this chapter is to describe a way of linking the scored item outcomes that resulted from the items design and the outcome space back to the construct that was the original inspiration for the items themselves—the way these connect is through the Wright map. This connection proceeds in two steps: (a) the item scores over a sample of respondent are used to estimate the respondent and item parameters on a scale using a statistical model, and then (b) the correspondence between the locations of the items on that scale and the waypoints of the construct map (i.e., on the Wright map) are used to establish public references for the scale (Mari et al., 2021). There have been many statistical models proposed and used in the last 100 years for the estimation step. In this book, the main approach taken is to explain and to use just one such model, the Rasch model, and the reasons for this focus are discussed in this chapter, but also in Chapter 10.  It is useful to know something about the historical background for these ideas, as that gives context to the basic ideas and terms used in measurement, as well as familiarize the reader with common vocabulary used by professionals in the area. Hence, this first section of the chapter will discuss two basic approaches to measurement and demonstrate how the construct modeling approach can be a way to reconcile them. The second section explains how the Wright map can be seen as an embodiment of the logic of the construct map and exemplifies how to interpret the empirical results in terms of the Wright map. This is followed by a section illustrating how these ideas play out for the case of the PF-10 example (Example 7 in Chapter 2). The account is didactic in nature rather than an attempt to present an exhaustive historical analysis. At the same time as the researchers mentioned below were working, there were others working on similar ideas and similar approaches. Not discussing them here is not intended to slight their contributions.