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

Area of Science:

• Psychometrics
• Statistics
• Data Analysis

Background:

• Descriptive fit indices aid in evaluating unrestricted or exploratory factor analytical (UFA) solutions, particularly for determining the number of common factors.
• While overall indices are common in UFA, especially for item analysis, difference indices are less prevalent.
• Raykov and collaborators introduced promising effect-size-type descriptive difference indices for UFA.

Purpose of the Study:

• To propose a relative version of Raykov's effect-size measure as a complement to the original absolute measure.
• To establish reference values for both indices in item-analysis contexts through simulation.
• To implement the proposed indices in R and a non-commercial factor analysis program.

Main Methods:

• Development of a relative difference index relating explained common variance to prior common factor variance.
• Simulation studies to establish reference values for the proposed and original indices in item analysis scenarios.
• Implementation of the indices in R and a widely used non-commercial factor analysis software.

Main Results:

• A novel relative difference index was proposed and implemented.
• Reference values for both the absolute and relative indices were established via simulation for item analysis.
• The practical utility of the proposed indices was demonstrated using an empirical dataset.

Conclusions:

• The proposed relative difference index serves as a valuable complement to existing measures for evaluating UFA solutions.
• The established reference values provide practical guidance for applying these indices in item analysis.
• The implementation in R and other software facilitates the adoption of these new descriptive fit indices.