Improving the Use of Parallel Analysis by Accounting for Sampling Variability of the Observed Correlation Matrix

Parallel analysis has been considered one of the most accurate methods for determining the number of factors in factor analysis. One major advantage of parallel analysis over traditional factor retention methods (e.g., Kaiser's rule) is that it addresses the sampling variability of eigenvalues obtained from the identity matrix, representing the correlation matrix for a zero-factor model. This study argues that we should also address the sampling variability of eigenvalues obtained from the observed data, such that the results would inform practitioners of the variability of the number of factors across random samples. Thus, this study proposes to revise the parallel analysis to provide the proportion of random samples that suggest <i>k</i> factors (<i>k</i> = 0, 1, 2, . . .) rather than a single suggested number. Simulation results support the use of the proposed strategy, especially for research scenarios with limited sample sizes where sampling fluctuation is concerning.