A Relative Normed Effect-Size Difference Index for Determining the Number of Common Factors in Exploratory Solutions

Descriptive fit indices that do not require a formal statistical basis and do not specifically depend on a given estimation criterion are useful as auxiliary devices for judging the appropriateness of unrestricted or exploratory factor analytical (UFA) solutions, when the problem is to decide the most appropriate number of common factors. While overall indices of this type are well known in UFA applications, especially those intended for item analysis, difference indices are much more scarce. Recently, Raykov and collaborators proposed a family of effect-size-type descriptive difference indices that are promising for UFA applications. As a starting point, we considered the simplest measure of this family, which (a) can be viewed as absolute and (b) from which only tentative cutoffs and reference values have been provided so far. In this situation, this article has three aims. The first is to propose a relative version of Raykov's effect-size measure, intended to be used as a complement of the original measure, in which the increase in explained common variance is related to the overall prior estimated amount of common factor variance. The second is to establish reference values for both indices in item-analysis scenarios using simulation. And the third aim (instrumental) is to implement the proposal in both R language and a well-known non-commercial factor analysis program. The functioning and usefulness of the proposal is illustrated using an existing empirical dataset.