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<p><b>New page</b></p><div>{{Short description|Diagnostic plot in multivariate statistics}}<br />
[[File:Screeplotr.png|thumb|250px|A sample scree plot produced in [[R (programming language)|R]]. The [[Kaiser criterion]] is shown in red.]]<br />
In [[multivariate statistics]], a '''scree plot''' is a line plot of the [[eigenvalue]]s of [[factor analysis|factor]]s or [[principal component]]s in an analysis.<ref name="LewithJonas2010">{{cite book|author1=George Thomas Lewith|author2=Wayne B. Jonas|author3=Harald Walach|title=Clinical Research in Complementary Therapies: Principles, Problems and Solutions|url=https://books.google.com/books?id=CSNw-spnFdkC&pg=PA354|date=23 November 2010|publisher=Elsevier Health Sciences|isbn=978-0-7020-4916-3|pages=354}}</ref> The scree plot is used to determine the number of factors to retain in an [[exploratory factor analysis]] (FA) or principal components to keep in a [[principal component analysis]] (PCA). The procedure of finding statistically significant factors or components using a scree plot is also known as a '''scree test'''. [[Raymond B. Cattell]] introduced the scree plot in 1966.<ref>{{cite journal |last1=Cattell |first1=Raymond B. |title=The Scree Test For The Number Of Factors |journal=Multivariate Behavioral Research |date=1966 |volume=1 |issue=2 |pages=245–276 |doi=10.1207/s15327906mbr0102_10 |pmid=26828106}}</ref><br />
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A scree plot always displays the eigenvalues in a downward curve, ordering the eigenvalues from largest to smallest. According to the scree test, the "elbow" of the graph where the eigenvalues seem to level off is found, and factors or components to the left of this point should be retained as significant.<ref name="DmitrienkoChuang-Stein2007">{{cite book|author1=Alex Dmitrienko|author2=Christy Chuang-Stein|author3=Ralph B. D'Agostino|title=Pharmaceutical Statistics Using SAS: A Practical Guide|url=https://books.google.com/books?id=FlXwIvSHND8C&pg=PA380|year=2007|publisher=SAS Institute|isbn=978-1-59994-357-2|pages=380}}</ref><br />
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As the "elbow" point has been defined as point of maximum curvature, this property has led to the creation of the Kneedle algorithm.<ref>{{cite conference |last1=Satopaa |first1=Ville |last2=Albrecht |first2=Jeannie |last3=Irwin |first3=David |last4=Raghavan |first4=Barath |date=2011-06-20 |title=Finding a "kneedle" in a haystack: Detecting knee points in system behavior |conference=2011 / 31st&nbsp;International Conference on Distributed Computing Systems |series=IEEE Workshops |publisher=[[Institute of Electrical and Electronics Engineers]] |pages=166–171 |doi=10.1109/ICDCSW.2011.20 |url=https://ieeexplore.ieee.org/document/5961514 |via=IEEE Explore|url-access=subscription }}</ref><br />
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== Etymology ==<br />
[[File:Yamnuska_bottom_cliff.jpg|right|150px|thumb|A scree at [[Mount Yamnuska]], [[Alberta]], [[Canada]]]]<br />
The scree plot is named after the elbow's resemblance to a [[scree]] in nature.<br />
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==Criticism==<br />
This test is sometimes criticized for its subjectivity. Scree plots can have multiple "elbows" that make it difficult to know the correct number of factors or components to retain, making the test [[reliability (statistics)|unreliable]]. There is also no standard for the scaling of the {{mvar|x}} and {{mvar|y}}&nbsp;axes, which means that different statistical programs can produce different plots from the same data.<ref name=NormanStreiner2007>{{cite book |author1=Norman, Geoffrey R. |author2=Streiner, David L. |date=15 September 2007|title=Biostatistics: The bare essentials |publisher=PMPH-USA |isbn=978-1-55009-400-8 |pages=201 |url=https://books.google.com/books?id=8rkqWafdpuoC&pg=PA201 |via=Google Books}}</ref><br />
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The test has also been criticized for producing too few factors or components for factor retention.{{clarify|date=April 2020}}<ref name=LewithJonas2010/><br />
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==See also==<br />
{{Commons category}}<br />
* [[Biplot]]<br />
* [[Parallel analysis]]<br />
* [[Elbow method (clustering)|Elbow method]]<br />
* [[Determining the number of clusters in a data set]]<br />
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==References==<br />
{{Reflist|25em}}<br />
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{{Statistics}}<br />
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[[Category:Statistical charts and diagrams]]<br />
[[Category:Factor analysis]]</div>imported>Staticshakedown