Confirmatory factor analysis

Confirmatory Factor Analysis (CFA) tests how well a pre-specified factor structure fits the data, reporting standard fit indices. Use CFA when you already have a hypothesised measurement model — for example, from prior theory or an Exploratory factor analysis.

When to use it

When you can state in advance which items load on which factor and want to judge how well that model fits.

Inputs

  • Variables — the numeric/ordinal items that make up your hypothesised factors.

  • Model — which items load on which factor.

Options

  • Estimator — Maximum Likelihood (ML) or Diagonally Weighted Least Squares (DWLS) (DWLS suits ordinal items).

  • Allow factor correlation — oblique (correlated factors) vs orthogonal.

  • Modification hints — adds a table of possible cross-loadings, ranked by the mean absolute standardized residual between an item and another factor’s indicators. These are residual-based hints, not exact Lagrange-multiplier modification indices.

  • Apply cross-loadings — a checklist of the current suggestions (and any already applied). Tick one to add that item as a cross-loading on the suggested factor; the model re-fits with it, and the loadings table then shows the item loading on both factors. Untick to revert.

Output

  • Fit indices — the standard measures used to judge how well the model reproduces the observed relationships.

  • Factor loadings for the specified structure.

  • With Plots on, a loadings heatmap and a factor-structure path diagram — factors right-aligned on the left, indicators left-aligned on the right, linked by their standardized loadings (factor correlations shown as links for oblique models). Its plot settings offer Vertical spacing and Horizontal distance sliders (which set the boxes’ separation without changing their size), an Arrow color picker, an Arrow label size slider (the loading numbers), a Correlation curve slider (0 = straight, up to a full bulge for the factor-correlation links), and an Arrow width ∝ loading toggle (uniform arrows otherwise). The overall figure honours the shared Plot Size slider.

Notes

  • You need enough complete cases for a stable solution, and the model must be identified (each factor needs enough indicators).