Scree plot

In multivariate statistics, a scree plot is a line plot of the eigenvalues of factors or principal components in an analysis.[1] 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.[2]

A sample scree plot produced in R. The "Kaiser rule" criteria is shown in red.

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.[3]

Etymology

The scree plot is named after its resemblance to a scree after its elbow.

Criticism

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 unreliable. There is also no standard for the scaling of the x and y axes, which means that different statistical programs can produce different plots from the same data.[4]

The test has also been criticized for producing too few factors or components for factor retention.[1]

A more objective version of the scree test has been proposed called the Cattell–Nelson–Gorsuch scree test (CNG scree test).

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gollark: Netflix was looking at using it for movie posters in their applications.
gollark: There are plenty of applications where you can get away with "looks pretty much okay", too.
gollark: Well, you can ask people to not put irrelevant random images in, but they'll probably do it for some stupid reason, and it's good if they can at least be mildly more efficient about it.
gollark: There's JPEG-XL or something, which will apparently allow *lossless* higher-efficiency representation of existing JPEGs. Very exciting.

See also

References
  1. George Thomas Lewith; Wayne B. Jonas; Harald Walach (23 November 2010). Clinical Research in Complementary Therapies: Principles, Problems and Solutions. Elsevier Health Sciences. p. 354. ISBN 0-7020-4916-6.
  2. Cattell, Raymond B. (1966). "The Scree Test For The Number Of Factors". Multivariate Behavioral Research. 1 (2): 245–276. doi:10.1207/s15327906mbr0102_10. PMID 26828106.
  3. Alex Dmitrienko; Christy Chuang-Stein; Ralph B. D'Agostino (2007). Pharmaceutical Statistics Using SAS: A Practical Guide. SAS Institute. p. 380. ISBN 978-1-59994-357-2.
  4. Geoffrey R. Norman; David L. Streiner (15 September 2007). Biostatistics: The Bare Essentials. PMPH-USA. p. 201. ISBN 978-1-55009-400-8.
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