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==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), paralell analysis has the virtue of an objective decision criterion.<ref name="Zwick1986">{{cite journal |last1=Zwick |first1=William R. |last2=Velicer |first2=Wayne F. |title=Comparison of five rules for determining the number of components to retain. |journal=Psychological Bulletin |date=1986 |volume=99 |issue=3 |pages=432–442 |doi=10.1037/0033-2909.99.3.432}}</ref> Since its original publication, multiple variations of parallel analysis have been proposed.<ref name="Glorfeld2016">{{cite journal |last1=Glorfeld |first1=Louis W. |title=An Improvement on Horn's Parallel Analysis Methodology for Selecting the Correct Number of Factors to Retain |journal=Educational and Psychological Measurement |date=2 July 2016 |volume=55 |issue=3 |pages=377–393 |doi=10.1177/0013164495055003002|s2cid=123508406 }}</ref><ref name="Crawford2010">{{cite journal |last1=Crawford |first1=Aaron V. |last2=Green |first2=Samuel B. |last3=Levy |first3=Roy |last4=Lo |first4=Wen-Juo |last5=Scott |first5=Lietta |last6=Svetina |first6=Dubravka |last7=Thompson |first7=Marilyn S. |title=Evaluation of Parallel Analysis Methods for Determining the Number of Factors |journal=Educational and Psychological Measurement |date=September 2010 |volume=70 |issue=6 |pages=885–901 |doi=10.1177/0013164410379332|s2cid=63269411 }}</ref> 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.<ref name=Velicer>{{cite journal| last=Velicer| first=W.F.| title=Determining the number of components from the matrix of partial correlations| journal=Psychometrika| year=1976| volume=41| issue=3| pages=321–327| doi=10.1007/bf02293557| s2cid=122907389}}</ref>
[[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>
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