1. Math 5364/66 Notes Principal Components and Factor Analysis in SAS Jesse Crawford Department of Mathematics Tarleton State University

2. Setting for Principal Components

3. Typical Coordinate System

4. Principal Components

5. Relation to Eigenvectors

6. Implementation in R

7. Simulating the Data in SAS

10. Covariance Matrix in SAS

11. Principal Components in SAS

12. Inputting a Covariance Matrix Manually

13. PCA Using Original Data

14. Example: Math and Reading Exams

15. Example: Adelges (Winged Aphids) 19 variables 4 principal components needed to explain 90% of the total variation PCA can be used to reduce dimensionality

16. PCA Summary

17. Setting for Factor Analysis

19. Observed data (Random) Intercept Term (Constant) Factor loadings (Constant) Common factors (Random) Specific factors (Random)

20. Setting for Factor Analysis Observed data (Random, Observable) Intercept Term (Constant) Factor loadings (Constant) Common factors (Random) Specific factors (Random) Unobservable

25. Communality or Common variance Uniqueness or Specific variance

29. Principal Component Method for Factor Analysis

32. Estimating Factor Scores

34. Rotation of Factors