Exploratory factor analysis

Exploratory Factor Analysis (EFA) uncovers the latent factors behind a set of items — how many underlying factors a battery reflects, and which items load on which factor. Use it when you do not yet have a hypothesised structure; to test a structure you already have, see Confirmatory factor analysis.

When to use it

To discover how many underlying factors a battery of items reflects, and which items load on which factor.

Inputs

  • Variables — two or more numeric/ordinal items.

Options

  • Correlation — Pearson (from the raw data) or Polychoric (tetrachoric for binary items), the latter estimated in-house and better suited to ordinal Likert items. The chosen matrix drives the KMO/Bartlett checks, the eigenvalues, and the extraction.

  • Extraction method — Minimum Residual (MINRES), Maximum Likelihood (ML), or Principal Axis (PAF).

  • Rotation — none, varimax, promax, oblimin, quartimax, and others (oblique rotations allow correlated factors).

  • Number of factors — how many to extract.

  • Factor names — optional comma-separated labels for the factors (e.g. Anxiety, Mood). They replace the default F1, F2 … in every table and the loadings heatmap; blank or missing entries keep the default for that factor.

  • Kaiser normalisation, Verbal indicators in tables (adds a plain-language column to the sampling-adequacy table — a KMO/MSA adequacy word per row and a significance verdict for Bartlett), Number columns, Verbal report (dropdown for how much written interpretation), and Plots.

Output

  • Sampling adequacy — KMO (overall and per item) and Bartlett’s test, with plain-language adequacy labels when verbal indicators are on.

  • Eigenvalues and a scree plot.

  • Factor loadings with communalities and uniquenesses, plus a loadings heatmap.

  • Factor correlations and a structure matrix for oblique rotations.

Notes

  • The number of factors cannot exceed the number of variables, and you need enough complete cases for a stable solution.