1. Factor Analysis Dr. Michael R. Hyman

2. Grouping Variables into Constructs

3. Purpose • Data reduction • If high redundancy in measures • If construct measures require multiple items (e.g., store image) • Substantive interpretation

4. Marketing Applications • Market segmentation • Find underlying variables to group consumers • Product research • Find underlying attributes that influence choice • Advertising research/media usage • Pricing studies • Find characteristics of price-sensitive consumers

5. Background • No (in)dependent variables • Metric inputs and outputs • Operates on correlation matrix, so assumes variables related linearly • Assumes variables sufficiently intercorrelated • Sphericity and KMO tests

6. When Factor Analysis Will Be Beneficial

7. When Factor Analysis Will Not be Beneficial

8. Key Definitions • Factor • Linear combination of variables (derived variable) • Underlying dimension that explains correlations among set of variables • Factor score • Each subject’s score on derived variable • Used in subsequent analysis

9. Key Definitions (cont.) • Factor loadings • Correlation between factors and original variable (if standardized) • All original variables with high loading (near + 1.0 on same factor grouped together • Communality • Percent of variation in an original variable explained by all the factors used

10. Key Definitions (cont.) • Explained variance • Percent of variation in all the data explained by each factor (eigenvalue)

11. Stopping Rules • A priori determination • Eigenvalue > 1.0 • Break (elbow) in scree plot • Percent variance explained • Should be at least 60% • Split data, run both halves, and compare • Test statistical significance of eigenvalues • Problem: With n>200, many minor factors will seem significant

12. Improve Interpretation by Rotating Factors • Orthogonal • Varimax (maximum +1 and 0s) • Oblique • Regardless, factor names are subjective

13. Steps in Conducting a Factor Analysis

14. Example #1: Item Set

15. Results: Example #1

16. Factor 1 Example #2: Factor Loadings for Attitudes toward Discount Stores Factor 2 Factor 3 Factor 4 Factor 5