Transformation Plots

The different levels at which each variable can be scaled impose restrictions on the quantifications. Transformation plots illustrate the relationship between the quantifications and the original categories resulting from the selected optimal scaling level.

The transformation plot for Neighborhood preference, which was treated as nominal, displays a U-shaped pattern, in which the middle category receives the lowest quantification, and the extreme categories receive values that are similar to each other. This pattern indicates a quadratic relationship between the original variable and the transformed variable. Using an alternative optimal scaling level is not suggested for Neighborhood preference.

Figure 1. Transformation plot for Neighborhood preference (nominal)

The quantifications for Newspaper read most often, in contrast, correspond to an increasing trend across the three categories that have observed cases. The first category receives the lowest quantification, the second category receives a higher value, and the third category receives the highest value. Although the variable is scaled as nominal, the category order is retrieved in the quantifications.

Figure 2. Transformation plot for Newspaper read most often (nominal)

Figure 3. Transformation plot for Age in years (ordinal)

The transformation plot for Age in years displays an S-shaped curve. The four youngest observed categories all receive the same negative quantification, whereas the two oldest categories receive similar positive values. Consequently, collapsing all younger ages into one common category (that is, below 50) and collapsing the two oldest categories into one category may be attempted. However, the exact equality of the quantifications for the younger groups indicates that restricting the order of the quantifications to the order of the original categories may not be desirable. Because the quantifications for the 26–30, 36–40, and 41–45 groups cannot be lower than the quantification for the 20–25 group, these values are set equal to the boundary value. Allowing these values to be smaller than the quantification for the youngest group (that is, treating age as nominal) may improve the fit. So although age may be considered an ordinal variable, treating it as such does not appear appropriate in this case. Moreover, treating age as numerical, and thus maintaining the distances between the categories, would substantially reduce the fit.