factoranalyses

Factor analyses are a family of statistical methods used to describe variability among observed variables in terms of fewer unobserved variables called factors. The aim is to identify latent constructs that influence the measured data. The approach is widely used in psychology, education, marketing, and other social sciences. Two main branches exist: exploratory factor analysis (EFA), which seeks to uncover the underlying structure without a predefined model, and confirmatory factor analysis (CFA), which tests a hypothesized factor structure.

Methodologically, factor analysis starts from a correlation or covariance matrix of continuous variables. Factors are estimated using methods such as maximum likelihood or principal axis factoring; principal components analysis is related but distinct, since it emphasizes total variance rather than shared variance among variables. After extraction, rotation is often applied to improve interpretability, with orthogonal rotations (e.g., varimax) yielding independent factors and oblique rotations (e.g., promax) allowing correlated factors. Outputs typically include factor loadings, communalities, and, for CFA, model fit indices and factor scores.

Process and interpretation involve determining how many factors to retain (rules of thumb include eigenvalues greater than 1, scree plots, and parallel analysis), followed by rotation and interpretation of factor loadings to identify the meaning of each factor.

Assumptions and data considerations include linear relationships among variables, suitable measurement scales, adequate sample size, and, for certain estimation methods, multivariate normality. Factor analysis is often used to validate scales, reduce dimensionality, and explore latent structures, while recognizing that results can be sensitive to sample, variables included, and methodological choices.

Historically, factor analysis traces to early work by Spearman on general intelligence, with later developments by Thurstone and others, and formalization through methods such as Kaiser’s criterion and Cattell’s scree test. CFA emerged later within the framework of structural equation modeling.