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Factor Analysis – Concept, Methods, and Applications
1. Introduction
📌 Factor Analysis (FA) is a statistical method used to identify underlying relationships between multiple observed variables.
📌 It reduces a large set of variables into a smaller set of factors while retaining essential information.
📌 Commonly used in economics, finance, psychology, and social sciences for data simplification and interpretation.
✔ Example: A researcher studies consumer behavior using 10 survey questions. Factor Analysis may reveal that these 10 questions relate to two main factors:
- “Brand Loyalty” (e.g., preference, trust, past purchases).
- “Price Sensitivity” (e.g., discounts, affordability).
2. Concept of Factor Analysis
✔ Factor Analysis assumes that correlated variables may be linked by a hidden common factor.
✔ Each observed variable is expressed as a linear combination of common factors and unique factors.
🔹 Mathematical Representation
For a set of p observed variables, the model is: Xi=λi1F1+λi2F2+…+λimFm+ϵiX_i = \lambda_{i1}F_1 + \lambda_{i2}F_2 + … + \lambda_{im}F_m + \epsilon_i
where:
- XiX_i = Observed variables
- FmF_m = Latent (unobservable) common factors
- λim\lambda_{im} = Factor loadings (weights)
- ϵi\epsilon_i = Unique factor (error term)
✔ Factor loadings (λ\lambda) indicate how strongly a variable is related to a factor.
3. Types of Factor Analysis
🔹 (1) Exploratory Factor Analysis (EFA)
✔ Used when no prior hypothesis exists about the structure of data.
✔ Finds hidden patterns and determines the number of factors.
✔ Example: Identifying the key skills that determine employee productivity.
🔹 (2) Confirmatory Factor Analysis (CFA)
✔ Used when a specific hypothesis exists about the relationship between variables.
✔ Tests whether a predefined factor structure fits the data.
✔ Example: A bank assumes that customer satisfaction depends on “Service Quality” and “Interest Rates” → CFA tests this assumption.
4. Methods of Factor Extraction
🔹 (1) Principal Component Analysis (PCA)
✔ Reduces dimensionality while preserving most of the variance.
✔ Constructs new uncorrelated variables (Principal Components).
✔ Used when the goal is data compression.
🔹 (2) Common Factor Analysis (CFA)
✔ Extracts only shared variance among variables.
✔ Best for identifying hidden constructs in social sciences.
🔹 (3) Maximum Likelihood Factor Analysis
✔ Assumes data follows a normal distribution.
✔ Estimates factor structure based on probability models.
✔ Used in econometrics and market research.
5. Factor Rotation Techniques
Once factors are extracted, rotation improves interpretation by simplifying factor loadings.
🔹 (1) Orthogonal Rotation (Varimax, Quartimax, Equamax)
✔ Factors remain uncorrelated.
✔ Varimax → Maximizes variance across factors, making interpretation easier.
🔹 (2) Oblique Rotation (Promax, Oblimin)
✔ Allows factors to be correlated.
✔ Used when underlying factors are not independent (e.g., in psychology).
6. Interpretation of Factor Analysis Results
📌 Example Output (Customer Satisfaction Survey Analysis)
| Survey Question | Factor 1: Service Quality | Factor 2: Pricing |
|---|---|---|
| Staff friendliness | 0.85 | 0.12 |
| Store cleanliness | 0.79 | 0.08 |
| Price fairness | 0.11 | 0.83 |
| Discount offers | 0.10 | 0.76 |
✔ Interpretation:
- Factor 1 (Service Quality) → High loadings for staff friendliness & cleanliness.
- Factor 2 (Pricing) → High loadings for price fairness & discount offers.
- Business Insight: Customer satisfaction is driven by two major factors: Service Quality and Pricing.
7. Applications of Factor Analysis
✔ Economics → Identifying key macroeconomic indicators affecting growth.
✔ Finance → Analyzing risk factors influencing stock returns.
✔ Marketing → Understanding customer preferences and segmentation.
✔ Psychology → Measuring personality traits.
✔ Healthcare → Identifying common symptoms of a disease.
8. Advantages & Limitations of Factor Analysis
✅ Advantages
✔ Reduces complexity by summarizing data.
✔ Helps in hypothesis generation and model development.
✔ Removes multicollinearity, improving regression models.
❌ Limitations
✖ Requires large datasets for accuracy.
✖ Results depend on subjective interpretation of factors.
✖ Sensitive to outliers and missing data.
9. Conclusion
✔ Factor Analysis simplifies complex data by identifying hidden relationships.
✔ Exploratory (EFA) vs. Confirmatory (CFA): Used for discovering vs. testing factor structures.
✔ PCA, Maximum Likelihood, and Rotations enhance interpretation.
✔ Widely used in economics, finance, marketing, and psychology.