Determining the number of factors using parallel analysis and its recent variants: Comment on Lim and Jahng (2019)

Lim and Jahng (2019) recently reported simulations supporting the conclusion that traditional parallel analysis (PA) performs more reliably than do more recent PA versions, particularly in the presence of minor factors acting as population error. With noise factors, correct identification of the number of main factors may, however, mean retaining a noise dimension at the expense of missing a signal dimension. This is documented to occur in nearly 17% of the authors' conditions involving noise factors; these cases did not deserve qualifying as successes. In this context, the reported tendency of other methods to include more dimensions than just the number of main factors (especially with increasing sample size) could mean that they indeed recuperated the full main factor dimensions. Some of these methods actually implement statistical testing of the null hypotheses that, for increasing values of k, the data could have been generated by a suitably determined k-factor model. When this is achieved, the data eigenvalue at rank k + 1 occupies a random rank among the same-rank eigenvalues from surrogate data generated according to the k-factor model. When k is insufficient, the data eigenvalue ranks high among those from the surrogate data. Achim (2017) already established that, for this purpose, iterative re-estimation of the communalities is more efficient than squared multiple regression to produce a suitable k-factor model and that eigenvalue-ranking works better with full than with reduced correlation matrices. This method is termed Next Eigenvalue Sufficiency Test (NEST); code is available with the original article. (PsycInfo Database Record (c) 2021 APA, all rights reserved).