Patil Vivek H, Surendra N. Singh, Sanjay Mishra, and D. Todd Donavan (2017). Parallel Analysis Engine to Aid in Determining Number of Factors to Retain using R [Computer software], available from https://analytics.gonzaga.edu/parallelengine/.
Based on parameters provided by the researcher, this engine calculates eigenvalues from randomly generated correlation matrices. These can be then compared with eigenvalues extracted from the researcher's dataset. The number of factors to retain will be the number of eigenvalues (generated from the researcher’s dataset) that are larger than the corresponding random eigenvalues (Horn 1965).
The default (and recommended) values for number of random correlation matrices and percentile of eigenvalues are 100 and 95 respectively (see Cota et al. 1993; Glorfeld 1995; Turner 1998; Velicer et al. 2000). Based on the nature of their particular dataset, researchers, can override these default options. Higher (lower) values of number of correlation matrices generated increase (decrease) computation time but provide more (fewer) data points in the distribution of different eigenvalues. The percentile determines the desired eigenvalue from this distribution, which is then used for comparison purposes. Lower values of the percentile tend to lead to over extraction (extraction of more factors than necessary).