Some Theory and Applications of Confirmatory Second-Order Factor Analysis

This paper shows how confirmatory factor analysis can be used to test second- (and higher-) order factor models in the areas of the structure of abilities, allometry, and the separation of specific and error variance estimates. In the latter area, an idea of Joreskog's is extended to include a new conceptualization of the estimation of validity. Second-order models are placed in a hierarchy of factor analysis models, which shows how the fit of various models can be compared. The concept of discriminability is introduced to describe a situation in which two models may both be identified, and yet the goodness-of-fit for both will be the same. This problem can usually be avoided by careful design of a study. Several examples are discussed.