Exploratory Factor Analysis (EFA) is a multivariate statistical technique that identifies clusters of correlated variables and represents them as manifestations of a smaller number of unobserved (latent) factors. In psychology, EFA has been instrumental in developing theories of intelligence, personality, and psychopathology by revealing the dimensional structure underlying test performance.
The Factor Model
The common factor model expresses each observed variable as a linear combination of common factors (shared across variables) plus a unique factor (specific to each variable): Xᵢ = λᵢ1 F₁ + λᵢ2 F₂ + ... + uᵢ. The factor loadings (λ) indicate how strongly each variable is related to each factor. The communality (h²) of each variable indicates the proportion of its variance explained by the common factors.
Key Decisions
Three critical decisions in EFA are: (1) how many factors to retain (parallel analysis is currently recommended over the Kaiser criterion or scree test), (2) which estimation method to use (maximum likelihood or principal axis factoring), and (3) how to rotate the solution (orthogonal rotations like varimax assume uncorrelated factors; oblique rotations like oblimin or promax allow correlations). In psychology, oblique rotation is usually preferable because psychological constructs are typically correlated.