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.