Category Quantifications
Recall that a discrimination measure is the variance of the quantified variable along a particular dimension. The discrimination measures plot contains these variances, indicating which variables discriminate along which dimension. However, the same variance could correspond to all of the categories being spread moderately far apart or to most of the categories being close together, with a few categories differing from this group. The discrimination plot cannot differentiate between these two conditions.
Category quantification plots provide an alternative method of displaying discrimination of variables that can identify category relationships. In this plot, the coordinates of each category on each dimension are displayed. Thus, you can determine which categories are similar for each variable.
Length in half-inches has five categories, three of which group together near the top of the plot. The remaining two categories are in the lower half of the plot, with the 2_1/2_in category very far from the group. The large discrimination for length along dimension 2 is a result of this one category being very different from the other categories of length. Similarly, for Head form, the category STAR is very far from the other categories and yields a large discrimination measure along the second dimension. These patterns cannot be illustrated in a plot of discrimination measures.
The spread of the category quantifications for a variable reflects the variance and thus indicates how well that variable is discriminated in each dimension. Focusing on dimension 1, the categories for Thread are far apart. However, along dimension 2, the categories for this variable are very close. Thus, Thread discriminates better in dimension 1 than in dimension 2. In contrast, the categories for Head form are spread far apart along both dimensions, suggesting that this variable discriminates well in both dimensions.
In addition to determining the dimensions along which a variable discriminates and how that variable discriminates, the category quantification plot also compares variable discrimination. A variable with categories that are far apart discriminates better than a variable with categories that are close together. For example, along dimension 1, the two categories of Brass are much closer to each other than the two categories of Thread, indicating that Thread discriminates better than Brass along this dimension. However, along dimension 2, the distances are very similar, suggesting that these variables discriminate to the same degree along this dimension. The discrimination measures plot discussed previously identifies these same relationships by using variances to reflect the spread of the categories.