Exploratory Factor Analysis (EFA)
EFA identifies latent factors that explain correlations among observed variables. Unlike PCA (dimension reduction), EFA assumes observed variables are caused by unobserved latent factors. Cornerstone of scale development and psychometric validation.
Step 1 — Provide your data
Observations x variables (numeric). Supports Excel Import, Sample Data Generator, and Manual Entry.
Step 2 — Configure the analysis
Number of factors: Auto (Kaiser) or Manual.
Extraction method:
| Method | Use when |
|---|---|
| Principal Axis Factoring (PAF) | Default; no normality assumption |
| Maximum Likelihood (ML) | Provides goodness-of-fit chi-square |
| Minimum Residual (MinRes) | When others have convergence issues |
Rotation method:
| Method | Type |
|---|---|
| Varimax | Orthogonal (most common) |
| Quartimax | Orthogonal (general factor) |
| Promax | Oblique (correlated factors) |
| Oblimin | Oblique |
Step 3 — Results
- KMO and Bartlett's diagnostics
- Eigenvalues with parallel analysis benchmarks
- Communalities (initial and extracted)
- Factor loadings (unrotated and rotated)
- Structure matrix and factor correlations (oblique)
- Cross-loadings flagged
- Model fit (ML only): chi-square, df, p-value
A UniversalChatBot is available for discussion.
Statistical methods used
PAF — iterative estimation replacing diagonal with SMCs.
ML — maximises likelihood; produces fit chi-square.
Varimax — maximises variance of squared loadings within factors (orthogonal).
Promax/Oblimin — allow correlated factors; return pattern + structure matrices.
Parallel Analysis — 100 Monte Carlo iterations; 95th percentile benchmark eigenvalues.
Cross-loading threshold — two largest loadings both > 0.4.
Loading interpretation: > 0.3 substantive, > 0.5 strong.