Choosing the Number of Dimensions

It is up to you to decide how many dimensions the solution should have. The scree plot can help you make this decision.

  1. To create a scree plot, from the menus choose:

    Analyze > Scale > Multidimensional Scaling (PROXSCAL)...

    Figure 1. Data Format dialog box
    The Multidimensional Scaling Data Format dialog box.
  2. In the Data Format dialog, select Multiple matrix sources in the Number of Sources group.
  3. Click Define.
    Figure 2. Multidimensional Scaling dialog box
    The Multidimensional Scaling main dialog box. What's selected?
  4. Select Aunt through Uncle (when variables are listed in file order) as proximities variables.
  5. Select sourceid as the variable identifying the source.
  6. Click Model.
    Figure 3. Model dialog box
    The Multidimensional Scaling Model dialog box.
  7. In the Model dialog, type 10 as the maximum number of dimensions.
  8. Click Continue.
  9. Click Restrictions in the Multidimensional Scaling dialog box.
    Figure 4. Restrictions dialog box
    The Multidimensional Scaling Restrictions dialog box
  10. Select Linear combination of independent variables.
  11. Click File to select the source of the independent variables.
  12. Select kinship_var.sav.
  13. Select gender, gener, and degree as restriction variables.

    Note that the variable gender has a user-missing value—9 = missing (for cousin). The procedure treats this as a valid category. Thus, the default linear transformation is unlikely to be appropriate. Use a nominal transformation instead.

  14. Select gender.
  15. Select Nominal from the Independent Variable Transformations drop-down list.
  16. Click Change.
  17. Click Continue.
  18. Click Plots in the Multidimensional Scaling dialog box.
    Figure 5. Plots dialog box
    The Multidimensional Scaling Plots dialog box.
  19. In the Plots dialog, select Stress in the Plots group.
  20. Click Continue.
  21. Click OK in the Multidimensional Scaling dialog box.
Figure 6. Scree plot
Scree plot

The procedure begins with a 10-dimensional solution and works down to a 2-dimensional solution. The scree plot shows the normalized raw stress of the solution at each dimension. You can see from the plot that increasing the dimensionality from 2 to 3 and from 3 to 4 offers large improvements in the stress. After 4, the improvements are rather small. You will choose to analyze the data by using a 3-dimensional solution, because the results are easier to interpret.

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