Partial Least Squares

Component Evaluation - Loading Plot

  

The loading plot is a scatterplot of the predictors projected onto the first and second components. It shows the x-loadings for the second component plotted against the x-loadings of the first component. Each point, representing a predictor, is connected to (0,0) on the plot.

The loading plot shows how important the predictors are to the first two components and is particularly useful when your predictors are on different scales. If the components explain most of the x-variance , which is shown in the Model Selection and Validation table, then the loading plot indicates how important the predictors are in the x-space. When considering the importance of the predictors in the entire model, you must also consider how much variance the components explain in the responses. To check this, examine the Rimage\squared.gif and predicted Rimage\squared.gif values in the Model Selection and Validation table.

Note

If your model contains more than 2 components, you may want to plot the x-loadings of other components using Graph > Scatterplot. To do this, store the x-loading matrix and then copy the matrix into columns using Data > Copy > Matrix to Columns.

When examining this plot, look for:

·    Angles between the lines, which represent the correlation between the predictors. Smaller angles indicate predictors are highly correlated.

·    Predictors with longer lines, which have greater loadings in the first or second components and are more important in the model.

Example Output

image\plsr_22n.gif

Interpretation

In this example, the loading plot shows that the predictors are highly correlated, because the angles between the lines are small. The lines are almost the same length, indicating the predictors are equally important. On the first component, the predictors have similar positive loadings, indicating they are equally important. On the second component, the first three predictors have greater loadings than the rest.

Examining the Model Selection and Validation table shows that the first two components explain 99% of the variance in the x-space, 79% of the variance in moisture, and 10% of the variance in fat.