Faktoranalyser

Faktoranalyser (factor analysis) are statistical techniques used to describe variability in a set of observed variables with a smaller number of latent factors. The goals are data reduction and the identification of underlying constructs that give rise to observed responses.

There are two main forms: exploratory factor analysis (EFA) and confirmatory factor analysis (CFA). EFA seeks to uncover the factor structure without strong prior hypotheses, while CFA tests a specified model of how observed variables relate to latent factors. A standard model is x = Λf + ε, where x are observed variables, Λ is the loading matrix, f are latent factors, and ε are unique factors or errors.

Extraction and rotation: factors are estimated using methods such as principal axis factoring or maximum likelihood. After extraction, rotation—orthogonal methods like Varimax or oblique methods like Promax—simplifies interpretation by clustering high loadings on a few variables.

Assessment and use: guidance on the number of factors includes eigenvalues, scree plots, the Kaiser criterion, or parallel analysis. In CFA, fit indices such as RMSEA, CFI, and TLI are used. Assumptions include linear relationships and, for ML, multivariate normality; factors and errors are typically uncorrelated in the orthogonal case. Applications span psychology, education, and social sciences for scale development, construct validation, and data reduction. Limitations include subjectivity in naming factors and sensitivity to sample size and model specification.