Introduction to Factor Analysis
Factor analysis is a powerful statistical method used to uncover latent variables (hidden factors) that explain patterns in observed data. Developed by Thurstone in 1931, it helps researchers:
(toc) #title=(Table of content)
Reduce data complexity by grouping correlated variables.
Identify underlying structures (e.g., psychological traits, socioeconomic factors).
Validate measurement tools (e.g., surveys, questionnaires).
(Keywords: "exploratory factor analysis", "confirmatory factor analysis", "latent variables")
1. What Is Factor Analysis?
Factor analysis is a dimension-reduction technique that identifies clusters of related variables (factors) from large datasets.
🔹 Social Work Material – Essential guides and tools for practitioners.
🔹 Social Casework – Learn client-centered intervention techniques.
🔹 Social Group Work – Strategies for effective group facilitation.
🔹 Community Organization – Methods for empowering communities.
Key Terms
Latent Variable: Unobserved factor (e.g., "socioeconomic status").
Factor Loading: Correlation between a variable and a factor (≥0.3 is significant).
Eigenvalue: Variance explained by a factor (≥1 is meaningful).
Communality: Proportion of a variable’s variance explained by factors.
2. Types of Factor Analysis
2.1 Exploratory Factor Analysis (EFA)
Purpose: Discover hidden structures without prior hypotheses.
Steps:
Collect Data: Use Likert-scale surveys or categorical variables.
Check Correlations: Ensure variables are related (Bartlett’s test, KMO >0.6).
Extract Factors: Use Principal Component Analysis (PCA) or Maximum Likelihood.
Rotate Factors: Apply Varimax (orthogonal) or Oblimin (oblique) rotation.
Interpret: Name factors based on high-loading variables.
🔹 Social Casework – Learn client-centered intervention techniques.
🔹 Social Group Work – Strategies for effective group facilitation.
🔹 Community Organization – Methods for empowering communities.
2.2 Confirmatory Factor Analysis (CFA)
Purpose: Test pre-defined factor structures (e.g., validate a theory).
Steps:
Specify Model: Define which variables link to which factors.
Assess Fit: Use indices like RMSEA (<0.05), CFI (>0.95).
Refine: Modify model if fit is poor (e.g., remove low-loading items).
3. Key Concepts & Outputs
3.1 Factor Loadings
Rule of Thumb:
≥0.6: Strong
0.3–0.6: Moderate
<0.3: Weak (exclude)
3.2 Scree Plots & Eigenvalues
Scree Plot: Visualize eigenvalues to decide factor count (retain factors before the "elbow").
Kaiser Criterion: Keep factors with eigenvalues ≥1.
3.3 Communalities
High communality (>0.5) = Variable is well-explained by factors.
4. Real-World Applications
Psychology: Identify traits like the Big Five Personality Model.
Marketing: Group customer preferences (e.g., "Price Sensitivity" factor).
Healthcare: Reduce symptom variables into broader syndromes.
5. Common Mistakes to Avoid
Conclusion
Factor analysis transforms complex data into actionable insights by revealing hidden patterns. Whether you’re validating a survey or exploring new theories, mastering EFA and CFA enhances research rigor.
Ready to analyze your data? [Download our free factor analysis checklist] or ask questions in the comments!
FAQ Section
Q1: When should I use EFA vs. CFA?
A: Use EFA for exploratory research (no prior hypotheses) and CFA to test predefined structures.
Q2: What’s a good sample size for factor analysis?
A: Minimum 150 observations; 5–10 cases per variable.
Q3: How do I report factor analysis results?
A: Include:
Extraction method (e.g., PCA)
Rotation type (e.g., Varimax)
Factor loadings & communalities
Model fit indices (for CFA)
