Exploratory Factor Analysis using Stata

Introduction to Exploratory Factor Analysis (EFA)

• Technique to explore inner relationships among measured variables.
• Aim: Discern underlying factors accounting for relationships among observed variables.

Model Overview

• Example of a two-factor model shown:
  • Boxes: Represent measured/observed variables.
  • Ovals: Represent latent variables (underlying constructs).
  • Arrows: Indicate relationships between latent variables and observed variables.
  • Circles: Indicate measurement error (uniqueness).

Steps in EFA

1. Identify Measured Variables
   • Begin with observed variables (e.g., 6 measured variables).
2. Determine Number of Factors
   • Analyze relationships and intercorrelations among variables.
3. Perform Main Analysis
   • Retain determined number of factors.
4. Interpret Factors
   • Based on relationships between observed variables and latent factors.

EFA Process in Stata

Overview of Stata vs. SPSS

• Stata requires more command-line syntax compared to SPSS's drop-down menus.
• Familiarity with Stata commands is essential for effective analysis.

Data Overview

• Dataset: 301 seventh and eighth grade students (Helsinger and Swineford, 1939).
• Variables: Visual perception, cubes, lozenges, paragraph completion, sentence completion, word meaning.
• Initial hypothesis: Potential existence of verbal and spatial ability factors.

Initial Analysis Steps

1. Correlation Matrix
   • Check for significant correlations among variables (ideally > 0.30).
   • Avoid minimal correlations (close to zero) and collinearity issues.
2. Determinant of Correlation Matrix
   • Ensure determinant is > 0.0001 to avoid singularity issues.
3. Kaiser-Meyer-Olkin (KMO) Measure
   • Assess sampling adequacy (values: 0.7-0.8 are acceptable).
4. Bartlett's Test of Sphericity
   • Tests if correlation matrix is significantly different from identity matrix.

Determining Number of Factors

1. Eigenvalue Cutoff Rule
   • Retain factors with eigenvalues > 1 (Kaiser Criterion).
2. Scree Plot
   • Visual representation of eigenvalues to assist in determining factors.
3. Parallel Analysis
   • Compare eigenvalues from PCA with randomly generated eigenvalues.
4. Minimum Average Partial (MAP) Correlation
   • Requires additional package installation.
5. Model Comparisons using Maximum Likelihood Estimation
   • Compare multiple factor models using AIC and BIC indices.

Final Analysis and Interpretation

• Conduct final factor analysis using chosen number of factors (two-factor model).
• Use factor rotation (Varimax or Promax) to improve interpretability of results.
  • Varimax: Orthogonal rotation maintaining independence of factors.
  • Promax: Oblique rotation allowing for correlated factors.
• Interpret factor loadings to define factors:
  • Factor 1: Represents verbal ability (high loadings from paragraph, sentence completion, and word meaning).
  • Factor 2: Represents spatial ability (high loadings from visual perception, cubes, and lozenges).

Additional Analysis Techniques

• Generate structure matrix and communality values for deeper insights into relationships.
• Report correlations among factors and other relevant statistics for thorough analysis.

Conclusion

• EFA is a complex process requiring strategic thought and careful implementation.
• Stata provides powerful tools for performing EFA, but users must be comfortable with syntax and command structures.
• Factors identified (verbal and spatial abilities) demonstrate the utility of EFA in understanding underlying data structures.