Parallel analysis

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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.[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]

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.[7]

Implementation

Parallel analysis has been implemented in JASP, SPSS, SAS, STATA, and MATLAB[8][9][10] and in multiple packages for the R programming language, including the psych[11][12] multicon,[13] hornpa,[14] and paran packages.[15][16]

See also

References

  1. ↑ Horn, John L. (June 1965). "A rationale and test for the number of factors in factor analysis". Psychometrika 30 (2): 179–185. doi:10.1007/bf02289447. PMID 14306381. 
  2. ↑ Mike Allen (11 April 2017). The SAGE Encyclopedia of Communication Research Methods. SAGE Publications. pp. 518. ISBN 978-1-4833-8142-8. https://books.google.com/books?id=4GFCDgAAQBAJ&pg=PA518. 
  3. ↑ 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. 
  4. ↑ 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. 
  5. ↑ 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. 
  6. ↑ Velicer, W.F. (1976). "Determining the number of components from the matrix of partial correlations". Psychometrika 41 (3): 321–327. doi:10.1007/bf02293557. 
  7. ↑ 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. 
  8. ↑ 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. 
  9. ↑ O'Connor, Brian. "Programs for Number of Components and Factors". https://people.ok.ubc.ca/brioconn/nfactors/nfactors.html. 
  10. ↑ O’connor, Brian P. (September 2000). "SPSS and SAS programs for determining the number of components using parallel analysis and Velicer's MAP test". Behavior Research Methods, Instruments, & Computers 32 (3): 396–402. doi:10.3758/BF03200807. PMID 11029811. 
  11. ↑ Revelle, William (2007). Determining the number of factors: the example of the NEO-PI-R. http://www.personality-project.org/r/book/numberoffactors.pdf. 
  12. ↑ Revelle, William (8 January 2020). "psych: Procedures for Psychological, Psychometric, and PersonalityResearch". https://cran.r-project.org/web/packages/psych/. 
  13. ↑ Sherman, Ryne A. (2 February 2015). "multicon: Multivariate Constructs". https://cran.r-project.org/web/packages/multicon/index.html. 
  14. ↑ Huang, Francis (3 March 2015). "hornpa: Horn's (1965) Test to Determine the Number of Components/Factors". https://cran.r-project.org/web/packages/hornpa/index.html. 
  15. ↑ Dinno, Alexis. Gently Clarifying the Application of Horn's Parallel Analysis to Principal Component Analysis Versus Factor Analysis. https://alexisdinno.com/Software/files/PA_for_PCA_vs_FA.pdf. 
  16. ↑ Dinno, Alexis (14 October 2018). paran: Horn's Test of Principal Components/Factors. https://cran.r-project.org/web/packages/paran/. 




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