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Factor Analysis – Concept & Interpretation
1. Introduction
📌 Factor Analysis is a statistical technique used to identify underlying factors (latent variables) that explain patterns of correlations among observed variables.
📌 It helps reduce dimensionality while preserving essential information.
📌 Used in economics, psychology, marketing, finance, and social sciences.
✔ Example: In consumer behavior research, purchase decisions may depend on unobserved factors like brand perception, price sensitivity, and product quality.
2. Concept of Factor Analysis
✔ Factor analysis assumes that multiple observed variables are influenced by a smaller number of unobserved (latent) factors.
✔ The goal is to reduce the dataset’s complexity by finding common patterns.
🔹 (1) Factor Model
The general mathematical representation is: Xi=λi1F1+λi2F2+…+λikFk+ϵiX_i = \lambda_{i1} F_1 + \lambda_{i2} F_2 + … + \lambda_{ik} F_k + \epsilon_i
where:
- XiX_i = Observed variables
- λij\lambda_{ij} = Factor loadings (strength of the relationship)
- FkF_k = Latent factors
- ϵi\epsilon_i = Unique (random) error term
✔ Factor loadings (λ\lambda) represent the correlation between observed variables and underlying factors.
✔ Higher loadings → Stronger influence of the factor on that variable.
3. Types of Factor Analysis
🔹 (1) Exploratory Factor Analysis (EFA)
✔ Used when the underlying structure of data is unknown.
✔ Identifies how many factors exist and which variables are linked to each factor.
✔ Commonly used in market research, psychology, and sociology.
✔ Example: A company wants to group customer preferences into hidden factors like “Price Sensitivity” and “Brand Loyalty.”
🔹 (2) Confirmatory Factor Analysis (CFA)
✔ Used when the structure is already known or hypothesized.
✔ Tests whether observed variables align with predefined factors.
✔ Commonly used in survey validation and hypothesis testing.
✔ Example: A bank expects customer satisfaction to depend on service quality, interest rates, and digital banking experience, and uses CFA to verify this.
4. Steps in Factor Analysis
✔ Step 1: Data Collection → Collect multiple related variables.
✔ Step 2: Correlation Matrix → Analyze relationships between variables.
✔ Step 3: Extract Factors → Use Principal Component Analysis (PCA) or Eigenvalue analysis.
✔ Step 4: Rotate Factors → Use Varimax Rotation to improve interpretation.
✔ Step 5: Interpret Factor Loadings → Identify significant relationships.
5. Interpretation of Factor Analysis Results
✔ Factor Loadings (λ\lambda):
- Values close to 1 → Strong relationship between variable and factor.
- Values close to 0 → Weak relationship.
✔ Eigenvalues: - Measure how much variance a factor explains.
- Factors with eigenvalues >1 are retained.
✔ Communalities: - Indicate how much of a variable’s variance is explained by the factors.
- Higher values (>0.5) indicate better representation.
📌 Example Output from Factor Analysis:
| Variable | Factor 1 (Brand Loyalty) | Factor 2 (Price Sensitivity) |
|---|---|---|
| Purchase Frequency | 0.85 | 0.10 |
| Brand Preference | 0.82 | 0.12 |
| Sensitivity to Discounts | 0.18 | 0.80 |
| Willingness to Pay More | 0.12 | 0.78 |
✔ Interpretation:
- “Purchase Frequency” and “Brand Preference” are strongly associated with Brand Loyalty.
- “Sensitivity to Discounts” and “Willingness to Pay More” are linked to Price Sensitivity.
- The two hidden factors successfully explain customer behavior.
6. Applications of Factor Analysis
✔ Economics: Identifying key economic indicators affecting GDP growth.
✔ Marketing: Understanding consumer preferences and segmenting markets.
✔ Finance: Identifying hidden risk factors affecting stock prices.
✔ Psychology: Identifying personality traits from survey data.
7. Conclusion
✔ Factor Analysis reduces complexity by identifying hidden relationships in data.
✔ Helps in market segmentation, economic forecasting, and behavioral analysis.
✔ Interpretation of factor loadings and eigenvalues is crucial for meaningful insights.