Building Hierarchies of Factors with Disjoint Factor Analysis

Hierarchical and higher-order models are a useful way to assess underlying concepts that involve nested groups of observable variables. By assuming that there is a hierarchical relationship among these observable variables, a broader underlying concept can be represented as a tree-like structure, where each internal node represents a different level of abstraction for the concept being measured. In this chapter, we introduce a novel method for modeling these unknown hierarchical structures of observable variables, called higher-order disjoint factor analysis. This approach is both exploratory and nested and is estimated sequentially. Each subset of observable variables is modeled to be reliable and internally consistent, which means that variables related to a specific factor consistently measure a unique theoretical construct. The new method is employed to build hierarchies of factors for the Holzinger–Swineford 24-variable data set. A final discussion completes the chapter.