Raîche, Gilles × Walls, Theodore A. Magis, David Riopel, Martin Blais, Jean - Guy #
Hogrefe Publishing Corp.
Methodology vol:9 issue:1 pages:23-29
Most of the strategies that have been proposed to determine the number of components that account for the most variation in a
principal components analysis of a correlation matrix rely on the analysis of the eigenvalues and on numerical solutions. The Cattell’s scree test is
a graphical strategy with a nonnumerical solution to determine the number of components to retain. Like Kaiser’s rule, this test is one of the most
frequently used strategies for determining the number of components to retain. However, the graphical nature of the scree test does not
definitively establish the number of components to retain. To circumvent this issue, some numerical solutions are proposed, one in the spirit of
Cattell’s work and dealing with the scree part of the eigenvalues plot, and one focusing on the elbow part of this plot. A simulation study
compares the efficiency of these solutions to those of other previously proposed methods. Extensions to factor analysis are possible and may be
particularly useful with many low-dimensional components.