Object Scores

The object scores for the three-dimensional solution are plotted in a scatterplot matrix. In a scatterplot matrix, every dimension is plotted against every other dimension in a series of two-dimensional scatterplots. Note that the first two eigenvalues in three dimensions are not equal to the eigenvalues in the two-dimensional solution; in other words, the solutions are not nested. Because the eigenvalues in dimensions 2 and 3 are now smaller than 1 (giving a Cronbach’s alpha that is negative), you should prefer the two-dimensional solution. The three-dimensional solution is included for purposes of illustration.

Figure 1. Three-dimensional object scores scatterplot matrix
Three-dimensional object scores scatterplot matrix

The top row of plots reveals that the first dimension separates PRIMARY GROUPS and MOBS from the other groups. Notice that the order of the objects along the vertical axis does not change in any of the plots in the top row; each of these plots employs dimension 1 as the y axis.

The middle row of plots allows for interpretation of dimension 2. The second dimension has changed slightly from the two-dimensional solution. Previously, the second dimension had three distinct clumps, but now the objects are more spread out along the axis.

The third dimension helps to separate MOBS from PRIMARY GROUPS, which did not occur in the two-dimensional solution.

Look more closely at the dimension 2 versus dimension 3 and dimension 1 versus dimension 2 plots. On the plane defined by dimensions 2 and 3, the objects form a rough rectangle, with CROWDS, MODERN COMMUNITY, SECONDARY GROUPS, and PUBLIC at the vertices. On this plane, MOBS and PRIMARY GROUPS appear to be convex combinations of PUBLIC-CROWDS and SECONDARY GROUPS-MODERN COMMUNITY, respectively. However, as previously mentioned, they are separated from the other groups along dimension 1. AUDIENCES is not separated from the other groups along dimension 1 and appears to be a combination of CROWDS and MODERN COMMUNITY.

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