Scree Plot

A scree plot is a graphical tool used in the selection of the number of relevant components or factors to be considered in a principal components analysis or a factor analysis. Proposed originally by Raymond Cattell in 1966 in his article The Scree Test for the Number of Factors, the scree plot has become a widely used tool to deal with the issue of component and factor selection. Conceptually, the scree plot is a way of visualizing the magnitude of the variability associated with each one of the components extracted in a principal component analysis. This plot allows researchers to examine the pattern of decreasing variability attributable to each successive component in order to inform the selection of how many such components should be considered relevant for interpretation in a principal component analysis or extracted for inclusion in a subsequent factor analysis.

The scree plot takes its name from the characteristic pattern observed in these plots which resembles a mountain side that becomes less and less steep, until it flattens as it reaches the debris and loose stones at its base. In his article, Cattell described the rationale for the name as follows:

The use of a scree plot as a method for component selection relies on the visual judgment of the pattern observed in the plot, specifically the separation between the components that are part of the scree from the relevant components to the left of it, as opposed to alternative component selection methods that do not rely on subjective judgement by using, for instance, a specific cut point (e.g., the Kaiser rule), a statistical test (e.g., Bartlett’s chi-square test), or a computational procedure (e.g., parallel analysis).

Figure 1 shows an example of a scree plot produced through a principal component analysis of a data set of responses to the 50 items of the Big Five Personality Inventory. This example shows the traditional pattern resembling a steep mountainside created in this case by the first five extracted components, followed by the flatter scree produced by the remaining components. It is possible to argue that Figure 1 shows a double scree, the first one occurring between Components 6 and 8 and a [Page 1483]larger one starting on Component 9, but considering that the theory behind the instrument that is being analyzed, it is reasonable to adopt the five component solution based on the break in the slope that occurs after the higher scree.

Figure 1 A scree plot example from a principal components analysis of the 50 items of the Big Five Personality Inventory with data from the International Personality Item Pool.

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