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