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

Abstract

Past research suggests revised parallel analysis (R-PA) tends to yield relatively accurate results in determining the number of factors in exploratory factor analysis. R-PA can be interpreted as a series of hypothesis tests. At each step in the series, a null hypothesis is tested that an additional factor accounts for zero common variance among measures in the population. Integration of an effect size statistic—the proportion of common variance (PCV)—into this testing process should allow for a more nuanced interpretation of R-PA results. In this article, we initially assessed the psychometric qualities of three PCV statistics that can be used in conjunction with principal axis factor analysis: the standard PCV statistic and two modifications of it. Based on analyses of generated data, the modification that considered only positive eigenvalues ( ${\hat{\pi }}_{\mathrm{SMC}:\mathrm{k}\prime }^{+\hat{\Lambda }}$ ) overall yielded the best results. Next, we examined PCV using minimum rank factor analysis, a method that avoids the extraction of negative eigenvalues. PCV with minimum rank factor analysis generally did not perform as well as ${\hat{\pi }}_{\mathrm{SMC}:\mathrm{k}\prime }^{+\hat{\Lambda }}$ , even with a relatively large sample size of 5,000. Finally, we investigated the use of ${\hat{\pi }}_{\mathrm{SMC}:\mathrm{k}\prime }^{+\hat{\Lambda }}$ in combination with R-PA and concluded that practitioners can gain additional information from ${\hat{\pi }}_{\mathrm{SMC}:\mathrm{k}\prime }^{+\hat{\Lambda }}$ and make more nuanced decision about the number of factors when R-PA fails to retain the correct number of factors.