Whenever factors are correlated, there is, naturally, a question as to whether there truly are several independent factors or whether there is a single “higher-order” factor.[1] This has been a point of discussion for many decades, and is often conceptually and theoretically important. For example, is self-concept a single thing, or several separate things? Is depression a single construct composed of several subconstructs, or is it really not a coherent construct?

Scholars writing in this area since the early 20th century have argued that when initial factor analyses (we can refer to these as “first-order” factors as they come from the first level of analysis) produce correlated factors, researchers should explore whether there are second- or higher-order factors in order to more fully explicate the model (e.g., Gorsuch, 1983; Thompson, 2004).

There are at least two issues with higher-order factors that we need to address. The first is how to perform the analysis and interpret the results. The second issue is more conceptual: if initial EFA produces imperfect abstractions (unobservable variables called factors) that might or might not be precise representations of population dynamics, then higher-order factor analysis would entail analyzing these imperfect abstractions to create possibly more imperfect higher-order abstractions. This makes us a bit uneasy, particularly in an exploratory framework. Given how volatile and unpredictable the results of EFA can be, it seems that taking those results and analyzing them again doubles (or raises to a power) the risk of going awry and far afield of the true character of the population dynamics.

Another issue is whether there is a meaningful conceptual distinction between a single unitary factor or a multifactor construct with a unitary higher-order factor. We should seek to operate under principles of parsimony—in other words, if you as a scholar cannot meaningfully communicate why this distinction is important, you might want to ask whether it is worthwhile to pursue.

Since almost all factors are correlated in the population, the assertion that this analysis needs to take place under these conditions should be regarded carefully. Researchers must decide (a) whether higher-order exploratory analyses are desirable and (b) how strong a correlation warrants this extra exploration. If factors are correlated around r = 0.25 (about 6.25% overlap), is that enough of a correlation to justify higher-order analysis? What about r = 0.40, which equates to only 16% overlap? In our opinion, it’s difficult to define what a second-order factor is.