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Applied Statistics Using SPSS

Applied Statistics Using SPSS. Topic: Factor Analysis By Prof Kelly Fan, Cal State Univ, East Bay. Outline. Introduction Principal component analysis Rotations Using communalities other than one. Introduction. Reduce data

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Applied Statistics Using SPSS

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  1. Applied Statistics Using 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 happiness (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 • 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?

  6. Data Set:

  7. Data Set:

  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

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

  11. SPSS Output

  12. SPSS Output

  13. A Visual Tool: Component Plot (Loading plots in SPSS)

  14. Discussion • Q4 & Q6 are highly and positively correlated and so should be at the same direction of any factor (here component 1 & 2) • Similarly, the other questions should be at the same direction of factor 1 & 2 (component 1 & 2) • Need a rotation!!

  15. Rotation: Varimax Method

  16. Varimax rotation

  17. Before and After Rotation

  18. Rotation: Promax Method (optional) • Used when factors (depression/happiness) are allowed to be correlated (non-orthogonal)

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

  20. Un-weighted Least Squares • Initial communality of a question is the R^2 (squared multiple correlation) of regressing all others against this question

  21. Before and After Varimax Rotation

  22. Varimax rotation

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