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Factor Analysis

Factor Analysis. Grouping Variables into Constructs. Purpose. Data reduction If high redundancy in measures If construct measures require multiple items (e.g., store image) Substantive interpretation. Marketing Applications. Market segmentation Find underlying variables to group consumers

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Factor Analysis

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  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

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