Louis Guttman formulated the first radex model of intelligence, which he revised often. In his last update, Guttman and Levy (1991) distinguished among different kinds of test content modalities (verbal, numerical, geometrical), different kinds of mental processes: rule induction, rule application, rule practice (learning), and different modes of expression in examinee performance: oral, manual manipulative, paper and pencil. Tests of any modality correlate highly if they involve rule induction but with rule application and rule practice, the tests tend to have lower correlations across test modality.
I have adapted one of Guttman & Levy’s figures below. Technically it is a cylindrex (a series of stacked radexes):
It is possible to represent the radex model as a path diagram. It has the advantage of being more precise in some ways but it fails to show that not all facets behave in the same way.
Guttman and Levy used the WISC-R but these findings were replicated and extended using the WISC-IV in a study by Cohen, Fiorello, and Farley, 2007.
Many other kinds of radex models have been proposed but probably the most influential has been that of Marshalek, Snow, & Lohman (1983). The center of the radex is conceptualized as “cognitive complexity” and corresponds to the g factor.