Parallel analysis, also known as Horn's parallel analysis, is a statistical method used to determine the number of components to keep in a principal component analysis or factors to keep in an exploratory factor analysis. It is named after psychologist John L. Horn, who created the method, publishing it in the journal Psychometrika in 1965.[1] The method compares the eigenvalues generated from the data matrix to the eigenvalues generated from a Monte-Carlo simulated matrix created from random data of the same size.[2]
Evaluation and comparison with alternatives
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.[3] Since its original publication, multiple variations of parallel analysis have been proposed.[4][5] 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.[6]
An extensive 2022 simulation study by Haslbeck and van Bork[8] found that parallel analysis was among the best-performing existing methods, but was slightly outperformed by their proposed prediction error-based approach.
^Zwick, William R.; Velicer, Wayne F. (1986). "Comparison of five rules for determining the number of components to retain". Psychological Bulletin. 99 (3): 432–442. doi:10.1037/0033-2909.99.3.432.
^Glorfeld, Louis W. (2 July 2016). "An Improvement on Horn's Parallel Analysis Methodology for Selecting the Correct Number of Factors to Retain". Educational and Psychological Measurement. 55 (3): 377–393. doi:10.1177/0013164495055003002. S2CID123508406.
^Crawford, Aaron V.; Green, Samuel B.; Levy, Roy; Lo, Wen-Juo; Scott, Lietta; Svetina, Dubravka; Thompson, Marilyn S. (September 2010). "Evaluation of Parallel Analysis Methods for Determining the Number of Factors". Educational and Psychological Measurement. 70 (6): 885–901. doi:10.1177/0013164410379332. S2CID63269411.
^Velicer, W.F. (1976). "Determining the number of components from the matrix of partial correlations". Psychometrika. 41 (3): 321–327. doi:10.1007/bf02293557. S2CID122907389.
^Tran, U. S.; Formann, A. K. (2009). "Performance of parallel analysis in retrieving unidimensionality in the presence of binary data". Educational and Psychological Measurement. 69: 50–61. doi:10.1177/0013164408318761. S2CID143051337.
^Hayton, James C.; Allen, David G.; Scarpello, Vida (29 June 2016). "Factor Retention Decisions in Exploratory Factor Analysis: a Tutorial on Parallel Analysis". Organizational Research Methods. 7 (2): 191–205. doi:10.1177/1094428104263675. S2CID61286653.
