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Dr. Michael R. Hyman Factor Analysis
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2 Grouping Variables into Constructs
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3 Purpose Data reduction –If high redundancy in measures –If construct measures require multiple items (e.g., store image) Substantive interpretation
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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
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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
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6 When Factor Analysis Will Be Beneficial
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7 When Factor Analysis Will Not be Beneficial
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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
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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
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10 Key Definitions (cont.) Explained variance –Percent of variation in all the data explained by each factor (eigenvalue)
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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
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12 Improve Interpretation by Rotating Factors Orthogonal Varimax (maximum +1 and 0s) Oblique Regardless, factor names are subjective
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13 Steps in Conducting a Factor Analysis
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14 Example #1: Item Set
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15 Results: Example #1
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16 Example #2: Factor Loadings for Attitudes toward Discount Stores Factor 1 Factor 2 Factor 3 Factor 4 Factor 5
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