Parallel Analysis Engine to Aid Determining Number of Factors to Retain (Patil, Singh, Mishra, and Donovan 2007)

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Citing this page: This web utility may be cited in the following manner [Please note that the utility will now be available at this new website: The older server is going to be decommissioned. PLEASE NOTE THIS NEW WEB ADDRESS FOR THE UTILITY] :

Patil, Vivek H., Surendra N. Singh, Sanjay Mishra,and D. Todd Donavan (2007), "Parallel Analysis Engine to Aid Determining Number of Factors to Retain [Computer software]. Available from; Utility developed as part of
Patil, Vivek H., Surendra N. Singh, Sanjay Mishra, and Todd Donovan (2008), “Efficient Theory Development and Factor Retention Criteria: A Case for Abandoning the ‘Eigenvalue Greater Than One’ Criterion,Journal of Business Research, 61 (2), 162-170.


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 using Principal Components Analysis) that are larger than the corresponding random eigenvalues (Horn 1965). The engine utilizes a SAS-based code written by O'Connor (2000).

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).

Please Enter Your Specifications:

Number of Variables in your Dataset to be Factor Analyzed

Sample Size of Your dataset              

Type of Analysis

  (default is ‘1’  [RECOMMENDED] for Principal components Analysis; Use '2' for Principal Axis Factoring)

Number of Random Correlation Matrices to Generate

  (default is 100)

Percentile of Eigenvalues                        

(default is 95)


(please modify as desired)


Select References

Horn, J. L. (1965), “A Rationale and Test For the Number of Factors in Factor Analysis,” Psychometrika, 30, 179-85.

O'Connor, Brian P. (2000), "SPSS and SAS Programs for Determining the Number of  Components Using Parallel Analysis and Velicer's MAP Test," Behavior Research Methods, Instruments and Computers, 32 (3), 396-402.

We thank Professor Brian O'Connor for the permission to utilize his program and appreciate the assistance provided by Patricia Oslund in the development of this engine.