When a PCA, PCR or PLS analysis has been performed it is not always evident how to determine which of the variables in the analysis are significant. In The Unscrambler® X, when doing such an analysis, a two-dimensional plot of the loadings is displayed in the Overview plots (unless the data have been designated as “spectra”, in which case the default plot is different). In the 2-D loadings plot it is not always easy to discern which variables are significant for explaining the variance in the data, as the scale of values may be different. With the Correlation Loadings plot the importance of individual variables is visualized more clearly than in the standard loadings plot.

Correlation loadings are computed for each variable for the displayed latent variables (PCs or factors). The 2-D plot contains two ellipses that indicate how much variance is taken into account by the model. The outer ellipse is the unit circle and indicates 100% explained variance. The inner ellipse indicates 50% of explained variance.

To access the Correlation Loadings plot the Loadings plot must be active. This can then be changed to the Correlation Loadings plot by using the icon Correlation Loadings plot icon

Correlation Loadings of variables along (PC1, PC2)
Correlation Loadings of variables along (PC1, PC2)

In the above plot five variables are located in the inner circle. They do not contain enough structured variation to be discriminating for the economic activity of different countries in the data set, explaining less than 50% of the variance in the data. The four variables in the radius between the ellipses are more discriminating for the samples being analyzed. Variables close to origin in the 2-D plot are not well explained by the components displayed in the given plot. Correlation loadings are also available for 1-D line loading plots. When a line plot is generated, the 1-D correlation loadings toolbar icon is displayed as follows 1-D correlation loadings toolbar icon

In the 1-D correlation loadings pot there are red dashed lines for the bounds of the 50 and 100% explained variance for the given latent variable. Values that lie within the upper and lower bounds of the plot are modelled by that latent variable. Those that lie between the two inner bounds are not. The 1-D correlation loading plots are especially useful when interpreting important wavelengths in the analysis of spectroscopic or contributing variables in time series data, as shown in the plot below.

Correlation Line Loadings of spectroscopic variables in Factor 1
Correlation Line Loadings of spectroscopic variables in Factor 1