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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).
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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.