multivariate statistics Multivariate statistics is a subdivision of statistics encompassing the simultaneous observation and analysis of more than one outcome variable, i.e., '' multivariate random variables''. Multivariate statistics concerns understanding the differ ...

, a scree plot is a line plot of the

eigenvalue In linear algebra, an eigenvector ( ) or characteristic vector is a vector that has its direction unchanged (or reversed) by a given linear transformation. More precisely, an eigenvector \mathbf v of a linear transformation T is scaled by a ...

s of

factor Factor (Latin, ) 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, such a factor is a resource used ...

s or

principal component Principal component analysis (PCA) is a linear dimensionality reduction technique with applications in exploratory data analysis, visualization and data preprocessing. The data is linearly transformed onto a new coordinate system such that th ...

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 Variable (research), variables. EFA is a technique within factor analysis whose overarching ...

(FA) or principal components to keep in a

principal component analysis Principal component analysis (PCA) is a linear dimensionality reduction technique with applications in exploratory data analysis, visualization and data preprocessing. The data is linearly transformed onto a new coordinate system such that th ...

(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 a

scree 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. The term ''scree'' is ap ...

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.

References

{{Statistics Statistical charts and diagrams Factor analysis

Etymology

Criticism

See also

References