1 Applied Statistics Using SAS and SPSS Topic: Factor Analysis By Prof Kelly Fan, Cal State Univ, East Bay

2 Outline Introduction Principal component analysis Rotations Using communalities other than one

3 Introduction Reduce data Summarize many ordinal categorical factors by a few combinations of them (new factors)

4 Example. 6 Questions Goal: a measure of depression and a measure of paranoia (how pleasant) 6 questions with response using number 1 to 7. The smaller the number is, the stronger the subject agrees. 4: no opinion

5 Example. 6 Questions 1.I usually feel blue. 2.People often stare at me. 3.I think that people are following me. 4.I am usually happy. 5.Someone is trying to hurt me. 6.I enjoy going to parties. Q. Which questions will a depressed person likely agree with? A happy person?

6 Data Set: Subj QuestionQuestion

7 Data Set: Subj QuestionQuestion

8 Principal Component Analysis Analyze >> Data Reduction >> Factor… The bigger the eigenvalue is, the more information this factor (component) carries.

9 A Visual Tool: Scree Plot

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11 Communalities Communalities represent how much variance in the original variables is explained by all of the factors kept in the analysis.

12 SPSS Output

13 Two Summary Factors

14 A Visual Tool: Component Plot

15 Discussion Q4 & Q6 should be at the same direction of factor 1 & 2 (component 1 & 2) The other questions should be at the same direction of factor 1 & 2 (component 1 & 2) Need a rotation!!

16 Rotation: Varimax Rotation

17 Varimax rotation

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20 Using Communalities Other Than One When the original factors are not equally important Different methods of “extraction”

21 Un-weighted Least Squares

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23 Varimax rotation