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In multivariate statistics
Multivariate statistics is a subdivision of statistics encompassing the simultaneous observation and analysis of more than one outcome variable.
Multivariate statistics concerns understanding the different aims and background of each of the dif ...
, a scree plot is a line plot of the eigenvalue
In linear algebra, an eigenvector () or characteristic vector of a linear transformation is a nonzero vector that changes at most by a scalar factor when that linear transformation is applied to it. The corresponding eigenvalue, often denoted ...
s of factor
Factor, a Latin word meaning "who/which acts", may refer to:
Commerce
* Factor (agent), a person who acts for, notably a mercantile and colonial agent
* Factor (Scotland), a person or firm managing a Scottish estate
* Factors of production, suc ...
s or principal component
Principal may refer to:
Title or rank
* Principal (academia), the chief executive of a university
** Principal (education), the office holder/ or boss in any school
* Principal (civil service) or principal officer, the senior management level ...
s in an analysis. The scree plot is used to determine the number of factors to retain in an exploratory factor analysis
In multivariate statistics, exploratory factor analysis (EFA) is a statistical method used to uncover the underlying structure of a relatively large set of variables. EFA is a technique within factor analysis whose overarching goal is to identify ...
(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.
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.
Etymology
The scree plot is named after the elbow's resemblance to ascree
Scree is a collection of broken rock fragments at the base of a cliff or other steep rocky mass that has accumulated through periodic rockfall. Landforms associated with these materials are often called talus deposits. Talus deposits typically ...
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. The test has also been criticized for producing too few factors or components for factor retention. 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.See also
*Biplot
Biplots are a type of exploratory graph used in statistics, a generalization of the simple two-variable scatterplot.
A biplot overlays a ''score plot'' with a ''loading plot''.
A biplot allows information on both samples and variables of a d ...
* Parallel analysis 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 psycholog ...
* Elbow method
*Determining the number of clusters in a data set Determining the number of clusters in a data set, a quantity often labelled ''k'' as in the ''k''-means algorithm, is a frequent problem in data clustering
Cluster analysis or clustering is the task of grouping a set of objects in such a way th ...
References
{{Statistics Statistical charts and diagrams Factor analysis