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The parallel analysis method for determining the number of components to retain in a principal components analysis has received a recent resurgence of support and interest. However, researchers and practitioners desiring to use this criterion have been hampered by the required Monte Carlo analyses needed to develop the criteria. Two recent attempts at presenting regression estimation methods to determine eigenvalues were found to be deficient in several respects, and less accurate in general, than a simple linear interpolation of tabled random data eigenvalues generated through Monte Carlo simulation. Other methods for determining the parallel analysis criteria are discussed.
Gary J. Lautenschlager (1989) studied this question.