Discrimination Measures
Before examining the rest of the object scores plots, let’s see if the discrimination measures agree with what we’ve said so far. For each variable, a discrimination measure, which can be regarded as a squared component loading, is computed for each dimension. This measure is also the variance of the quantified variable in that dimension. It has a maximum value of 1, which is achieved if the object scores fall into mutually exclusive groups and all object scores within a category are identical. (Note: This measure may have a value greater than 1 if there are missing data.) Large discrimination measures correspond to a large spread among the categories of the variable and, consequently, indicate a high degree of discrimination between the categories of a variable along that dimension.
The average of the discrimination measures for any dimension equals the percentage of variance accounted for that dimension. Consequently, the dimensions are ordered according to average discrimination. The first dimension has the largest average discrimination, the second dimension has the second largest average discrimination, and so on, for all dimensions in the solution.
As noted on the object scores plot, the discrimination measures plot shows that the first dimension is related to variables Thread and Bottom shape. These variables have large discrimination measures on the first dimension and small discrimination measures on the second dimension. Thus, for both of these variables, the categories are spread far apart along the first dimension only. Length in half-inches has a large value on the second dimension but a small value on the first dimension. As a result, length is closest to the second dimension, agreeing with the observation from the object scores plot that the second dimension seems to separate the longest objects from the rest. Indentation of head and Head form have relatively large values on both dimensions, indicating discrimination in both the first and second dimensions. The variable Brass, located very close to the origin, does not discriminate at all in the first two dimensions. This makes sense, since all of the objects can be made of brass or not made of brass.