**3.2 Output from NL.M.PCA**

**Table 3** shows the output of NL.M.PCA when NL.M.PCA is applied to Expectation data with *r* ¼ 5 of the number of PCs, proportion *P* as a criterion, and forwardbackward stepwise selection and *type* 3 quantifications as selection procedures. The number *q* is the number of selected variables and the value *P* is the criterion value. **Y**1|**Y**<sup>2</sup> shows that the left side of each row is the question numbers to be selected ð Þ **Y**<sup>1</sup> and the right side to be deleted ð Þ **Y**<sup>2</sup> . If you have a specific number *q* for variables to be used, such as 20, 10, or 2/3 = 24, 1/2 = 18, you can use variables whose numbers are displayed in **Y**<sup>1</sup> at that *q*. If the number of variables to be used is not determined, the proportion *P* can be used. For example, since the proportion *P* is 66.95% with all 35 variables, if you want to keep *P* up to 65%, looking at the row of *P* ¼ 0*:*6512 (i.e., *q* ¼ 20), you can use 20 variables in **Y**1. Alternatively, if the difference between the proportion with all 35 variables and that with selected variables should be less than 1%, 25 variables can be used because 0*:*6695 � 0*:*01 ¼ 0*:*6595, which is the *P* value at


**Table 3.** *Selection results (expectations, r* ¼ 5*, proportion P, forward-backward stepwise selection, Type 3).*

**Figure 1.** *Change of the proportion P for every q (from 35 to 5).*

*q* ¼ 25. **Figure 1** shows the change of *P* for every *q*. This graph can be used to obtain guidance on the determination of the number of variables. Looking at this graph, if there is a large drop in *P*, the number of variables just before that point can be used (for this data, no particular drop is observed).

When using *RV*, the same considerations are applied, and scatter plots are also considered to see how close the configurations are.
