Exploratory Factor Analysis (EFA)

They look similar and are often confused, but they model different things. PCA reduces dimensions by capturing the total variance of the items, treating components as composites of the observed variables. EFA models only the common variance shared among items, treating the observed items as reflections of underlying latent factors plus item-specific error. If your goal is to recover latent constructs, use EFA; if you only need data compression, PCA may suffice.

EFA is exploratory: it discovers how many factors there are and which items load on which factor, without imposing that pattern in advance. CFA (confirmatory factor analysis) is confirmatory: you specify the factor structure ahead of time and test how well it fits. A common workflow is to explore the structure with EFA, then validate it with CFA on a new, independent sample.

The eigenvalue > 1 (Kaiser) rule and the scree plot are widely used but heuristic and can over- or under-extract. Parallel analysis is the preferred, more objective criterion. Interpretability of the rotated solution should also guide the final choice.

Use an orthogonal rotation such as varimax when you assume the factors are uncorrelated, and an oblique rotation such as oblimin when you expect the factors to correlate. Rotation makes the loadings easier to interpret without changing the communalities or the overall fit.