Parallel analysis

Parallel analysis is regarded as one of the more accurate methods for determining the number of factors or components to retain. In particular, unlike early approaches to dimensionality estimation (such as examining scree plots), parallel analysis has the virtue of an objective decision criterion. In a Monte Carlo simulation study across 96 conditions with known component structure, Zwick and Velicer found that parallel analysis and Velicer's MAP test generally outperformed the other methods tested, while the Kaiser rule tended to severely overestimate the number of components. Since its original publication, multiple variations of parallel analysis have been proposed. Other methods of determining the number of factors or components to retain in an analysis include the scree plot, Kaiser rule, or Velicer's MAP test. Anton Formann provided both theoretical and empirical evidence that parallel analysis's application might not be appropriate in many cases since its performance is influenced by sample size, item discrimination, and type of correlation coefficient. An extensive 2022 simulation study by Haslbeck and van Bork found that parallel analysis was among the best-performing existing methods, but was slightly outperformed by their proposed prediction error-based approach. ==Implementation==