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# Learning Objectives - Understand factor analysis concepts and purpose - Apply PCA for dimensionality reduction - Interpret factor loadings and rotation output - Correlation and covariance concepts - Linear algebra basics ## 1. What is Factor Analysis?
Learning Objectives
- Understand factor analysis concepts and purpose
- Apply PCA for dimensionality reduction
- Interpret factor loadings and rotation output
- Correlation and covariance concepts
- Linear algebra basics
1. What is Factor Analysis?
Intuition: Survey questions may measure underlying hidden factors (latent constructs). For example, 10 questions about customer experience may actually measure 3 underlying factors: Service Quality, Product Quality, and Value.
Purpose:
- Data reduction (reduce many variables to fewer factors)
- Identify underlying structure (which variables group together)
- Construct validation (verify that survey measures what it intends)
- Create factor scores for further analysis (segmentation, regression)
2. Factor Extraction Methods
Principal Component Analysis (PCA): Extracts factors that maximize variance explained. Most common. Uses all variance (common + unique).
Principal Axis Factoring (PAF): Focuses on common variance only. Better for identifying latent constructs.
Eigenvalue (Kaiser Criterion): Retain factors with eigenvalue > 1. Eigenvalue = variance explained by that factor. A factor should explain at least as much variance as one variable.
Scree Plot: Plot eigenvalues against factor number. Look for "elbow" where the curve flattens. Factors before the elbow are retained.
Total Variance Explained: Percentage of total variance accounted for by retained factors. Aim for at least 60%.
3. Factor Rotation
Varimax (Orthogonal): Factors uncorrelated. Simplifies interpretation (each variable loads strongly on only one factor). Most common.
Oblimin (Oblique): Factors allowed to correlate. More realistic for social science (attitudes are usually correlated). Produces simpler structure.
Factor Loading: Correlation between variable and factor. |Loading| > 0.4 = significant, > 0.6 = strong. Loadings squared = variance in variable explained by factor.
Q1: What is the purpose of factor analysis?Reduce many variables to fewer underlying factors, identify structure in data, validate survey constructs (e.g., show that questions intended to measure "satisfaction" actually group together). Q2: What does a factor loading of 0.7 mean?Strong correlation (0.7) between the variable and the factor. Squared loading = 0.49, meaning the factor explains 49% of the variable's variance. Q3: Why rotate factors? Compare varimax and oblimin.Rotation simplifies interpretation by making loadings more extreme (high higher, low lower) while preserving fit. Varimax: factors uncorrelated (simpler). Oblimin: factors can correlate (more realistic). Q4: What is the Kaiser criterion?Retain factors with eigenvalue > 1. The rationale: each factor should explain at least as much variance as a single standardized variable (which has variance = 1). Q5: What is KMO and what value is adequate?Kaiser-Meyer-Olkin measure of sampling adequacy. Ranges 0-1. KMO > 0.6 = adequate for factor analysis. KMO > 0.8 = excellent. Values below 0.5 suggest FA is not appropriate. Join Discord PreviousData Analysis & Hypothesis TestingNextCluster Analysis