An Investigation of the Parallel Analysis Criterion for Determining the Number of Common Factors

Then correlation matrices based upon real and random data with squared multiple correlations in the diagonals are factored, the hypothesis is that the point at which the curves of the latent roots cross indicates the number of common factors. Sampling studies confirm the hypothesis when the common factor model provides a good fit to the data. When small overlapping, nonrandom factors are introduced, the expected value of the number of common factors can still be the number of major factor in the population when the nonrandom "noise" is small compared to sampling error "noise." This criterion for the number of common factors, furthermore, is more accurate than the method of maximum likelihood.