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