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Factor Analysis

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  1. Factor Analysis

  2. Description • Goal: Discover m < p underlying Factors (aka latent variables) from Covariances or Correlations among p observed variables • Makes use of Principal Components and Rotation to obtain the Factors • Exploratory Factor Analysis: Using observed responses to obtain factor structure. • Confirmatory Factor Analysis: Uses new data to determine whether hypothesized Factor structure is appropriate.

  3. Orthogonal Factor Model - I

  4. Orthogonal Factor Model - II

  5. Example 1

  6. Example 2

  7. Estimation – Principal Factor Method - I

  8. Estimation – Principal Factor Method - II

  9. Selecting m, the Number of Retained Factors

  10. Maximum Likelihood Estimation I – Normal F, e

  11. Maximum Likelihood Estimation – Normal F, e

  12. Large-Sample Test for # of Common Factors (m)

  13. Factor Rotation

  14. Estimating Factor Scores – Weighted Least Squares

  15. Estimating Factor Scores – Regression Approach - I

  16. Estimating Factor Scores – Regression Approach - II

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