Editing Factor analysis (section)

==== Older methods ====
Kaiser criterion: The Kaiser rule is to drop all components with eigenvalues under 1.0 – this being the eigenvalue equal to the information accounted for by an average single item.<ref name="Kaiser1960">{{cite journal |last1=Kaiser |first1=Henry F. |title=The Application of Electronic Computers to Factor Analysis |journal=Educational and Psychological Measurement |date=April 1960 |volume=20 |issue=1 |pages=141–151 |doi=10.1177/001316446002000116|s2cid=146138712 }}</ref> The Kaiser criterion is the default in [[SPSS]] and most [[statistical software]] but is not recommended when used as the sole cut-off criterion for estimating the number of factors as it tends to over-extract factors.<ref>{{cite book |first1=D.L. |last1=Bandalos |first2=M.R. |last2=Boehm-Kaufman |chapter=Four common misconceptions in exploratory factor analysis |editor1-first=Charles E. |editor1-last=Lance |editor2-first=Robert J. |editor2-last=Vandenberg |title=Statistical and Methodological Myths and Urban Legends: Doctrine, Verity and Fable in the Organizational and Social Sciences |chapter-url=https://books.google.com/books?id=KFAnkvqD8CgC&pg=PA61 |year=2008 |publisher=Taylor & Francis |isbn=978-0-8058-6237-9 |pages=61–87}}</ref> A variation of this method has been created where a researcher calculates [[confidence interval]]s for each eigenvalue and retains only factors which have the entire confidence interval greater than 1.0.<ref name="Warne, R. T. 2014">{{cite journal | last1 = Warne | first1 = R. T. | last2 = Larsen | first2 = R. | year = 2014 | title = Evaluating a proposed modification of the Guttman rule for determining the number of factors in an exploratory factor analysis | journal = Psychological Test and Assessment Modeling | volume = 56 | pages = 104–123 }}</ref><ref>{{cite journal | last1 = Larsen | first1 = R. | last2 = Warne | first2 = R. T. | year = 2010 | title = Estimating confidence intervals for eigenvalues in exploratory factor analysis | journal = Behavior Research Methods | volume = 42 | issue = 3| pages = 871–876 | doi = 10.3758/BRM.42.3.871 | pmid = 20805609 | doi-access = free }}</ref>

[[Scree plot]]:<ref>{{cite journal|first1=Raymond |last1=Cattell|journal=Multivariate Behavioral Research|volume=1|number=2|pages=245–76|year=1966|title=The scree test for the number of factors|doi=10.1207/s15327906mbr0102_10|pmid=26828106}}</ref>
The Cattell scree test plots the components as the X-axis and the corresponding [[eigenvalue]]s as the [[Y-axis]].  As one moves to the right, toward later components, the eigenvalues drop. When the drop ceases and the curve makes an elbow toward less steep decline, Cattell's scree test says to drop all further components after the one starting at the elbow. This rule is sometimes criticised for being amenable to researcher-controlled "[[Wiktionary:fudge factor|fudging]]".  That is, as picking the "elbow" can be subjective because the curve has multiple elbows or is a smooth curve, the researcher may be tempted to set the cut-off at the number of factors desired by their research agenda.{{Citation needed|date=March 2016}}

Variance explained criteria: Some researchers simply use the rule of keeping enough factors to account for 90% (sometimes 80%) of the variation.  Where the researcher's goal emphasizes [[Occam's razor|parsimony]] (explaining variance with as few factors as possible), the criterion could be as low as 50%.