Factor Analysis

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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 subjects 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 gt 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 ngt200, 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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Factor 1
Example 2 Factor Loadings for Attitudes toward
Discount Stores
Factor 2
Factor 3
Factor 4
Factor 5