Parallel analysis explained

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

Notes and References

  1. Horn . John L. . A rationale and test for the number of factors in factor analysis . Psychometrika . June 1965 . 30 . 2 . 179–185 . 10.1007/bf02289447 . 14306381. 19663974 .
  2. Book: Mike Allen. The SAGE Encyclopedia of Communication Research Methods. 11 April 2017. SAGE Publications. 978-1-4833-8142-8. 518.
  3. Zwick . William R. . Velicer . Wayne F. . Comparison of five rules for determining the number of components to retain. . Psychological Bulletin . 1986 . 99 . 3 . 432–442 . 10.1037/0033-2909.99.3.432.
  4. Glorfeld . Louis W. . An Improvement on Horn's Parallel Analysis Methodology for Selecting the Correct Number of Factors to Retain . Educational and Psychological Measurement . 2 July 2016 . 55 . 3 . 377–393 . 10.1177/0013164495055003002. 123508406 .
  5. Crawford . Aaron V. . Green . Samuel B. . Levy . Roy . Lo . Wen-Juo . Scott . Lietta . Svetina . Dubravka . Thompson . Marilyn S. . Evaluation of Parallel Analysis Methods for Determining the Number of Factors . Educational and Psychological Measurement . September 2010 . 70 . 6 . 885–901 . 10.1177/0013164410379332. 63269411 .
  6. Velicer. W.F.. Determining the number of components from the matrix of partial correlations. Psychometrika. 1976. 41. 3. 321–327. 10.1007/bf02293557. 122907389.
  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 . 10.1177/0013164408318761 . 143051337 .
  8. Hayton . James C. . Allen . David G. . Scarpello . Vida . Factor Retention Decisions in Exploratory Factor Analysis: a Tutorial on Parallel Analysis . Organizational Research Methods . 29 June 2016 . 7 . 2 . 191–205 . 10.1177/1094428104263675. 61286653 .
  9. Web site: O'Connor . Brian . Programs for Number of Components and Factors . people.ok.ubc.ca.
  10. O’connor . Brian P. . SPSS and SAS programs for determining the number of components using parallel analysis and Velicer's MAP test . Behavior Research Methods, Instruments, & Computers . September 2000 . 32 . 3 . 396–402 . 10.3758/BF03200807. 11029811 . free .
  11. Revelle . William . Determining the number of factors: the example of the NEO-PI-R . 2007 .
  12. Web site: Revelle . William . psych: Procedures for Psychological, Psychometric, and PersonalityResearch . 8 January 2020.
  13. Web site: Sherman . Ryne A. . multicon: Multivariate Constructs . 2 February 2015.
  14. Web site: Huang . Francis . hornpa: Horn's (1965) Test to Determine the Number of Components/Factors . 3 March 2015.
  15. Dinno . Alexis . Gently Clarifying the Application of Horn's Parallel Analysis to Principal Component Analysis Versus Factor Analysis .
  16. Dinno . Alexis . paran: Horn's Test of Principal Components/Factors . 14 October 2018 .

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