## 441: Scree Plots

The scree plots show the percentage of variance explained by each X and/or Y mode. The percentages are shown for all modes regardless of the numbers that were specified for use. The plots can be useful in selecting the appropriate number(s) of X and Y modes to retain. One method for selecting the number of modes involves identifying "elbows" in the scree plot. The number of modes up to, but not including, the elbow are retained on the basis that the additional modes explain similar amounts of variance, which are assumed to be largely noise. Elbows are often easier to identify when the percentage variance is plotted on a logarithmic axis. An option to use logarithmic axes is available by right-clicking on the scree plots. Another simple method for selecting the number of modes is to retain a sufficient number to ensure that the total variance retained exceeds a predefined minimum. The cumulative percentage of variance explained by the modes can be shown using the Cumulative option by right-clicking on the scree plots.

Another method for selecting the number of models is to compare the explained variance of each mode to that expected from
random data. A computationally and conceptually simple such approach is based on the random stick theorem, which involves
randomly dividing the total variance into segments and considering the expected size of the
*
n
*
th largest segment. The
sizes of the random stick segments can be included on the scree plot by an option available by right-clicking on the plot.

The graph can be saved as a graphics file by right-clicking anywhere in the child window and selecting Export from the pop-up menu. A default name is given to the graphics file, but this name can be changed using the browse button. The image quality for all the graphics formats can be improved by increasing the size of the image (see Options ~ Graphics ~ Graph Scaling ).