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

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 ((pi) over cap (+(Lambda) over cap)(SMC:k')) 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 ((pi) over cap (+(Lambda) over cap)(SMC:k')), even with a relatively large sample size of 5,000. Finally, we investigated the use of ((pi) over cap (+(Lambda) over cap)(SMC:k')) in combination with R-PA and concluded that practitioners can gain additional information from ((pi) over cap (+(Lambda) over cap)(SMC:k')) and make more nuanced decision about the number of factors when R-PA fails to retain the correct number of factors.