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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]
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), 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]
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]
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]
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