Proportion of Indicator Common Variance Due to a Factor as an Effect Size Statistic in Revised Parallel Analysis

Area of Science:

• Psychometrics
• Statistical Analysis

Background:

• Exploratory Factor Analysis (EFA) relies on accurate factor number determination.
• Revised Parallel Analysis (R-PA) is a common method, but its interpretation can be enhanced.
• Effect size statistics, like Proportion of Common Variance (PCV), offer nuanced insights.

Purpose of the Study:

• To evaluate the psychometric properties of three PCV statistics for use with Principal Axis Factor Analysis (PAFA).
• To compare PCV performance with Minimum Rank Factor Analysis (MRFA).
• To investigate the combined utility of a modified PCV statistic and R-PA for factor retention decisions.

Main Methods:

• Assessed three PCV statistics, including a novel modification considering only positive eigenvalues.
• Analyzed generated data using PAFA and MRFA.
• Compared the performance of PCV statistics in conjunction with R-PA under varying conditions.

Main Results:

• The PCV modification considering only positive eigenvalues demonstrated superior performance with PAFA.
• PCV with MRFA was less effective than the modified PCV with PAFA, even with large sample sizes.
• Integrating the modified PCV statistic with R-PA provided valuable supplementary information for factor retention.

Conclusions:

• The modified PCV statistic, focusing on positive eigenvalues, is recommended for enhancing R-PA in EFA.
• Combining R-PA with this PCV measure aids practitioners in making more informed decisions regarding the number of factors.
• This approach improves the robustness of factor analysis by providing a more nuanced interpretation of results.