A Regression Equation for Determining the Dimensionality of Data.

Parallel analysis has received much support and attention as a criterion for using eigenvalues to determine the dimensionality of data. Parallel analysis compares sample eigenvalues to expected eigenvalues of a sample from a correlation matrix generated by independent normally distributed random variables. To make parallel analysis more accessible to researchers, several studies have proposed multiple regression equations for estimating the expected value of the eigenvalues of a sample correlation matrix assuming that the population correlation matrix is the identity matrix. A new regression equation to estimate the mean value of eigenvalues is presented in this article and a comparative study reveals favorable performance of this proposed equation to previously published regression equations. This proposed technique has the advantage that a table of coefficients, listing regression coefficients for each eigenvalue root, is not needed.