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[[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 response theory#The item response function|item discrimination]], and type of [[correlation coefficient]].<ref>{{cite journal | last1 = Tran | first1 = U. S. | last2 = Formann | first2 = A. K. | year = 2009 | title = Performance of parallel analysis in retrieving unidimensionality in the presence of binary data | journal = Educational and Psychological Measurement | volume = 69 | pages = 50–61 | doi = 10.1177/0013164408318761 | s2cid = 143051337 }}</ref>
An extensive 2022 simulation study by Haslbeck and van Bork<ref>{{Cite journal |last=Haslbeck |first=Jonas M. B. |last2=van Bork |first2=Riet |date=February 2024 |title=Estimating the number of factors in exploratory factor analysis via out-of-sample prediction errors. |url=https://doi.apa.org/doi/10.1037/met0000528 |journal=Psychological Methods |language=en |volume=29 |issue=1 |pages=48–64 |doi=10.1037/met0000528 |issn=1939-1463|url-access=subscription |doi-access=free }}</ref> found that parallel analysis was among the best-performing existing methods, but was slightly outperformed by their proposed prediction error-based approach.
==Implementation==
Parallel analysis has been implemented in [[JASP]], [[SPSS]], [[SAS (software)|SAS]], [[STATA]], and [[MATLAB]]<ref>{{cite journal |last1=Hayton |first1=James C. |last2=Allen |first2=David G. |last3=Scarpello |first3=Vida |title=Factor Retention Decisions in Exploratory Factor Analysis: a Tutorial on Parallel Analysis |journal=Organizational Research Methods |date=29 June 2016 |volume=7 |issue=2 |pages=191–205 |doi=10.1177/1094428104263675|s2cid=61286653 }}</ref><ref>{{cite web |last1=O'Connor |first1=Brian |title=Programs for Number of Components and Factors |url=https://people.ok.ubc.ca/brioconn/nfactors/nfactors.html |website=people.ok.ubc.ca |access-date=2020-04-10 |archive-date=2021-05-23 |archive-url=https://web.archive.org/web/20210523164754/https://people.ok.ubc.ca/brioconn/nfactors/nfactors.html |url-status=dead }}</ref><ref>{{cite journal |last1=O’connor |first1=Brian P. |title=SPSS and SAS programs for determining the number of components using parallel analysis and Velicer's MAP test |journal=Behavior Research Methods, Instruments, & Computers |date=September 2000 |volume=32 |issue=3 |pages=396–402 |doi=10.3758/BF03200807|pmid=11029811 |doi-access=free }}</ref> and in multiple packages for the [[R (programming language)|R programming language]], including the ''psych''<ref>{{cite journal |last1=Revelle |first1=William |title=Determining the number of factors: the example of the NEO-PI-R |date=2007 |url=http://www.personality-project.org/r/book/numberoffactors.pdf}}</ref><ref>{{cite web |last1=Revelle |first1=William |title=psych: Procedures for Psychological, Psychometric, and PersonalityResearch |url=https://cran.r-project.org/web/packages/psych/ |date=8 January 2020}}</ref> ''multicon'',<ref>{{cite web |last1=Sherman |first1=Ryne A. |title=multicon: Multivariate Constructs |url=https://cran.r-project.org/web/packages/multicon/index.html |date=2 February 2015}}</ref> ''hornpa'',<ref>{{cite web |last1=Huang |first1=Francis |title=hornpa: Horn's (1965) Test to Determine the Number of Components/Factors |url=https://cran.r-project.org/web/packages/hornpa/index.html |date=3 March 2015}}</ref> and ''paran'' packages.<ref>{{cite journal |last1=Dinno |first1=Alexis |title=Gently Clarifying the Application of Horn's Parallel Analysis to Principal Component Analysis Versus Factor Analysis |url=https://alexisdinno.com/Software/files/PA_for_PCA_vs_FA.pdf}}</ref><ref>{{cite journal |last1=Dinno |first1=Alexis |title=paran: Horn's Test of Principal Components/Factors |date=14 October 2018 |url=https://cran.r-project.org/web/packages/paran/}}</ref> Parallel analysis can also be conducted in Mplus version 8.0 and forward.<ref>https://www.statmodel.com/HTML_UG/chapter16V8.htm</ref>
==See also==
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