ABSTRACT
Item response theory (IRT) provides a class of models describing the relationship between individual item responses and the construct(s) measured by the test. The central elements of an IRT model are that there is an unobservable (latent) variable such as ability or proficiency, usually called θ, that varies in the population of examinees (Lord, 1952), and that there is a trace line (Lazarsfeld, 1950) for each item response. The trace line is a function of θ; for dichotomously scored items (correct/incorrect), the trace line for the correct response is usually monotonically increasing as θ increases, and gives the varying probability of that response across the θ (ability/proficiency) continuum. Figure 4.1 shows trace lines (sometimes also called the item characteristic curves) for the correct response to several items. Trace lines for the correct response to the four spelling items. The heavy dashed lines represent the trace lines for girder for the reference group (on the left) and the focal group (on the right). The light solid lines represent the trace lines for infidelity, panoramic, and succumb (in left-to-right order); note that the trace line for panoramic is adjacent to (and obscured by) the trace line for girder for the reference group. https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203357811/d80c9e57-afa0-42f4-9a3a-a62c1516610b/content/fig4_1_B.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/>
