# Are composite factor scores produced by PCA are automatically standardize?

I have done a Principal Component Analysis (rotated factors, varimax, etc.) which gave me 6 factors (F1, F2, F3, F4, F5, and F6). From this PCA, I saved the factor scores for regression (In SPSS, I used during my Factor Analysis: Scores| Save as variables| Regression). From what I understand, the regression factor scores in SPSS are standardized, with a mean = 0 and Std deviation = 1 (correct me if I’m wrong). The output of the regression factors are as follow;

Descriptive Statistics
N   Range   Minimum Maximum Sum Mean    Std. Deviation
REGR factor score   1 for analysis 1    3063    11.01315    -6.39267    4.62048 .00000  .0000000    1.00000000
REGR factor score   2 for analysis 1    3063    11.32547    -2.29925    9.02622 .00000  .0000000    1.00000000
REGR factor score   3 for analysis 1    3063    9.35187 -5.19720    4.15467 .00000  .0000000    1.00000000
REGR factor score   4 for analysis 1    3063    11.58979    -4.17394    7.41585 .00000  .0000000    1.00000000
REGR factor score   5 for analysis 1    3063    23.94514    -4.10727    19.83787    .00000  .0000000    1.00000000
REGR factor score   6 for analysis 1    3063    11.26989    -2.97190    8.29799 .00000  .0000000    1.00000000
Valid N (listwise)  3063


Is it normal to have a result like above? Are the composite factor scores produced by SPSS are standardized?

Then I used the 6 factors as my independent variables along with other SES variables to explain BMI in multiple regression. How do I check for the absence of multicollinearity of the 6 factors, since r = 0?

• Are the composite factor scores produced by SPSS are standardized? 1) Yes, they are (always produced as) standardized - don't you see it?. 2) What do you mean saying "composite" here? If this is your word for "weighted sum" or "linear combination" then it is all right. – ttnphns Apr 21 '15 at 9:42
• SPSS saves PC scores standardized. But since you know component variances (the eigenvalues) you can always compute raw component scores out of standardized ones. – ttnphns Apr 21 '15 at 9:44

## 1 Answer

First, the output that you show shows that they are standardized. Each one has a mean of 0 and a standard deviation of 1 (last two columns of your output).

Second, if the only variables going into your regression were these orthogonal factor scores, you would not have to check for colinearity. But they might be colinear with your other variables - you can check using condition indexes as usual.