Scree plot explained

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 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 the elbow's resemblance to a scree in nature.

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 and  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]

As the "elbow" point has been defined as point of maximum curvature, as maximum curvature captures the leveling off effect operators use to identify knees, this has led to the creation of a Kneedle algorithm.[5]

See also

Notes and References

  1. Book: George Thomas Lewith. Wayne B. Jonas. Harald Walach. Clinical Research in Complementary Therapies: Principles, Problems and Solutions. 23 November 2010. Elsevier Health Sciences. 978-0-7020-4916-3. 354.
  2. Cattell . Raymond B. . The Scree Test For The Number Of Factors . Multivariate Behavioral Research . 1966 . 1 . 2 . 245–276 . 10.1207/s15327906mbr0102_10 . 26828106.
  3. Book: Alex Dmitrienko. Christy Chuang-Stein. Ralph B. D'Agostino. Pharmaceutical Statistics Using SAS: A Practical Guide. 2007. SAS Institute. 978-1-59994-357-2. 380.
  4. Book: Norman, Geoffrey R. . Streiner, David L. . 15 September 2007. Biostatistics: The bare essentials . PMPH-USA . 978-1-55009-400-8 . 201 . Google Books.
  5. Satopaa . Ville . Albrecht . Jeannie . Irwin . David . Raghavan . Barath . 2011-06-20 . Finding a "kneedle" in a haystack: Detecting knee points in system behavior . 2011 / 31st International Conference on Distributed Computing Systems . IEEE Workshops . . 166–171 . 10.1109/ICDCSW.2011.20 . IEEE Explore.