Introduction. Testlets as a multidimensional structure

One useful way to think about a test built of k testlets utilizes factor analytic vocabulary (Gessaroli & Folske, 2002). First, we note that all of the testlets contain information about the underlying trait of interest – a general factor. However, each of the items within a testlet also has some connection with the other items in that testlet, over and above the general factor – a testlet-specific factor. Thus, the factor structure of such a test has k + 1 orthogonal factors; a general factor, plus one factor for each testlet.

The story that describes a theoretical test structure, and its associated mode of analysis based on this concept, begins in 1937 with the publication of Karl Holzinger and Francis Swineford's bi-factor method. Holzinger and Swineford (1937) conceived of the bi-factor method as an extension of Spearman's two-factor model, and its character matched the conceptual structure that Thurstone had for his primary mental abilities (Thurstone, 1938). Specifically, they thought of the underlying structure of a bank of tests as consisting of a single general factor and each set of tests loading on its own specific factor. They illustrated this with a bank of 15 tests that all load on a single general factor of ability, but, in addition, had four tests that loaded on a spatial factor, three other tests that loaded on a mental speed factor, four tests on a motor speed factor, and the remaining four tests on a verbal factor.