Quantifications

For each variable, the quantifications, the vector coordinates, and the centroid coordinates for each dimension are presented. The quantifications are the values assigned to each category. The centroid coordinates are the average of the object scores of objects in the same category. The vector coordinates are the coordinates of the categories when they are required to be on a line, representing the variable in the object space. This is required for variables with the ordinal and numerical scaling level.

Figure 1. Quantifications for Intensity of interaction
Quantifications for Intensity of interaction
Figure 2. Joint plot category points
Joint plot with Dimension 2 on the vertical axis and Dimension 1 on the horizontal axis. Points are labeled with category values and colors indicate the variables

Glancing at the quantifications in the joint plot of the category points, you can see that some of the categories of some variables were not clearly separated by the categorical principal components analysis as cleanly as would have been expected if the level had been truly ordinal. Variables Intensity of interaction and Frequency of interaction, for example, have equal or almost equal quantifications for their two middle categories. This kind of result might suggest trying alternative categorical principal components analyses, perhaps with some categories collapsed, or perhaps with a different level of analysis, such as (multiple) nominal.

The joint plot of category points resembles the plot for the component loadings, but it also shows where the endpoints are located that correspond to the lowest quantifications (for example, slight for Intensity of interaction and none for Feeling of belonging). The two variables measuring interaction, Intensity of interaction and Frequency of interaction, appear very close together and account for much of the variance in dimension 1. Formality of Relationship also appears close to Physical Proximity.

By focusing on the category points, you can see the relationships even more clearly. Not only are Intensity of interaction and Frequency of interaction close, but the directions of their scales are similar; that is, slight intensity is close to slight frequency, and frequent interaction is near high intensity of interaction. You also see that close physical proximity seems to go hand-in-hand with an informal type of relationship, and physical distance is related to no relationship.

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