Path diagrams are wonderfully economical and precise methods of communicating the structure of a model. For example, Carroll’s (1993) Three Stratum Theory of Cognitive Abilities is usually shown with a diagram like this:
However, this model implies things that might not be strictly true. For example, it is possible that not all of the broad abilities (including g) are distinct entities. It is possible that some of them, to some degree, are what I have called hierarchical abstractions. The basic idea is that there might not be some general ability that applies to many different tasks. It is possible that certain distinct abilities tend to be used together in the same kinds of tasks, often forming a functional unity. For example, inductive and deductive (sequential) reasoning are rarely used separately. Rather, they are used in tandem to reach logical conclusions (in a syllogism, for example). Thus, it is reasonable to talk about a superordinate category of fluid reasoning even though it consists of distinct processes. So, in a much abbreviated form, Gf and Gc can conceptualized like so:
Of course, all the narrow abilities in the diagram might be abstractions themselves, consisting of many different sub-components.
I thought that it might be helpful to re-draw Carroll’s diagram in a way that does not commit us to thinking of the various constructs in the hierarchy as distinct abilities:
Carroll, J.B. (1993). Human cognitive abilities: A survey of factor-analytic studies. New York : Cambridge University Press.