Factor Analysis
Dr. Michael R. Hyman
Grouping
Variables
into
Constructs
2
Purpose
• Data reduction
– If high redundancy in measures
– If construct measures require multiple
items (e.g., store image)
• Substantive interpretation
3
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
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•
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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
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•
•
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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
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