Parallel Analysis Criteria: Revised Equations for Estimating the Latent Roots of Random Data Correlation Matrices

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Abstract
Regression equations may be used for estimating givenvalues to serve as parallel analysis criteria for determining the number of factors to retain. The accuracy of the first givenvalue's estimate directly influences the accuracy of subsequent estimates of given-values in regression equations derived to predict the latent roots of random data correlation matrices. Augmenting an equation presented by Allen and Hubbard (1986) with a variables-to-subjects ratio term leads to a significant improvement in predicting the first, as well as subsequent, givenvalues. Squared multiple correlations are .993 or higher for predicting all givenvalues. Parameter estimates for the augmented equation are presented to permit calculation of more nearly precise estimates of up to 48 givenvalues of a random data correlation matrix.