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Happiness comes not from material wealth but less desire.

Happiness comes not from material wealth but less desire. . Applied Statistics Using SAS . Topic: Factor Analysis By Prof Kelly Fan, Cal State Univ, East Bay. Outline. Introduction Principal component analysis Rotations. Introduction. Reduce data

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Happiness comes not from material wealth but less desire.

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  1. Happiness comes not from material wealth but less desire.

  2. Applied Statistics Using SAS Topic: Factor Analysis By Prof Kelly Fan, Cal State Univ, East Bay

  3. Outline • Introduction • Principal component analysis • Rotations

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

  5. 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

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

  7. Data Set:

  8. Data Set:

  9. Principal Component Analysis The bigger the eigenvalue is, the more information this factor (component) carries.

  10. A Visual Tool: Scree Plot

  11. Two Summary Factors

  12. Communalities • Communalities represent how much variance in the original variables is explained by all of the factors kept in the analysis (here the two factors)

  13. 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!!

  14. Rotation: Varimax Rotation

  15. Component Plot after Rotation

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

  17. SAS Code PROC FACTOR DATA=FACTOR PREPLOT PLOT ROTATE=VARIMAX NFACTORS=2 OUT=FACT SCREE; TITLE "Example of Factor Analysis"; VAR QUES1-QUES6; RUN;

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