Examining the Data

  1. To obtain a nonlinear canonical correlation analysis for this dataset, from the menus choose:

    Analyze > Dimension Reduction > Optimal Scaling...

    Figure 1. Optimal Scaling dialog box
    Optimal Scaling dialog box
  2. In the Optimal Scaling dialog, select Some variable(s) not multiple nominal in the Optimal Scaling Level group.
  3. Select Multiple sets in the Number of Sets of Variables group.
  4. Click Define.
    Figure 2. Nonlinear Canonical Correlation Analysis dialog box
    Nonlinear Canonical Correlation dialog with age and marital in the Set 1 Variables list
  5. Select Age in years and Marital status as variables for the first set.
  6. Select age and click Define Range and Scale.
    Figure 3. Define Range and Scale dialog box
    The Nonlinear Canonical Correlation Analysis Define Range and Scale dialog box.
  7. In the Define Range and Scale dialog, type 10 as the maximum value for this variable.
  8. Click Continue.
  9. In the Nonlinear Canonical Correlation Analysis dialog box, select marital and click Define Range and Scale.
  10. In the Define Range and Scale dialog, type 3 as the maximum value for this variable.
  11. Select Single nominal as the measurement scale.
  12. Click Continue.
  13. In the Nonlinear Canonical Correlation Analysis dialog box, click Next to define the next variable set.
    Figure 4. Nonlinear Canonical Correlation Analysis dialog box
    Nonlinear Canonical Correlation dialog box with pet and news in the Set 2 Variables list
  14. Select Pets owned and Newspaper read most often as variables for the second set.
  15. Select pet and click Define Range and Scale.
  16. In the Define Range and Scale dialog, type 5 as the maximum value for this variable.
  17. Select Multiple nominal as the measurement scale.
  18. Click Continue.
  19. In the Nonlinear Canonical Correlation Analysis dialog box, select news and click Define Range and Scale.
  20. In the Define Range and Scale dialog, type 5 as the maximum value for this variable.
  21. Select Single nominal as the measurement scale.
  22. Click Continue.
  23. In the Nonlinear Canonical Correlation Analysis dialog box, click Next to define the last variable set.
    Figure 5. Nonlinear Canonical Correlation Analysis dialog box
    The Nonlinear Canonical Correlation Analysis dialog box with music and live in the Set 3 Variables list
  24. Select Music preferred and Neighborhood preference as variables for the third set.
  25. Select music and click Define Range and Scale.
  26. In the Define Range and Scale dialog, type 5 as the maximum value for this variable.
  27. Select Single nominal as the measurement scale.
  28. Click Continue.
  29. In the Nonlinear Canonical Correlation Analysis dialog box, select live and click Define Range and Scale.
  30. In the Define Range and Scale dialog, type 3 as the maximum value for this variable.
  31. Select Single nominal as the measurement scale.
  32. Click Continue.
  33. In the Nonlinear Canonical Correlation Analysis dialog box, click Options.
    Figure 6. Options dialog box
    The Nonlinear Canonical Correlation Analysis Options dialog box.
  34. Deselect Centroids and select Weights and component loadings in the Display group.
  35. Select Category centroids and Transformations in the Plot group.
  36. Select Use random initial configuration.
  37. Click Continue.
  38. In the Nonlinear Canonical Correlation Analysis dialog box, click OK.

After a list of the variables with their levels of optimal scaling, categorical canonical correlation analysis with optimal scaling produces tables showing the frequencies of objects by category for each variable in the analysis. These tables are especially important if there are missing data, since almost-empty categories are more likely to dominate the solution. In this example, there are no missing data.

A second preliminary check is to examine the plot of object scores for outliers. Outliers have such different quantifications from the other objects that they will be at the boundaries of the plot, thus dominating one or more dimensions.

If you find outliers, you can handle them in one of two ways. You can simply eliminate them from the data and run the nonlinear canonical correlation analysis again. Alternatively, you can try recoding the extreme responses of the outlying objects by collapsing (merging) some categories.

As shown in the plot of object scores, there were no outliers for the survey data.

Figure 7. Object scores
Scatterplot of object scores with Dimension 2 on the vertical axis and Dimension 1 on the horizontal axis

Next