1. Dr. Michael R. Hyman Factor Analysis

2. 2 Grouping Variables into Constructs

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

4. 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. 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. 6 When Factor Analysis Will Be Beneficial

7. 7 When Factor Analysis Will Not be Beneficial

8. 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. 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. 10 Key Definitions (cont.) Explained variance –Percent of variation in all the data explained by each factor (eigenvalue)

11. 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. 12 Improve Interpretation by Rotating Factors Orthogonal Varimax (maximum +1 and 0s) Oblique Regardless, factor names are subjective

13. 13 Steps in Conducting a Factor Analysis

14. 14 Example #1: Item Set

15. 15 Results: Example #1

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