faktoranalytische

Faktoranalytische methods, often referred to as factor analysis, are statistical techniques used to identify latent variables that explain patterns of correlations among observed variables. The goal is data reduction and theory building: a smaller set of factors summarizes the structure underlying a larger set of measures.

There are two main branches: exploratory factor analysis (EFA) and confirmatory factor analysis (CFA). EFA aims to uncover the latent structure without imposing a predefined model, allowing factors to emerge from the data. CFA tests a specified factor structure and evaluates how well the model fits the observed data, providing fit indices and theory-driven constraints.

Key steps include assessing data suitability (e.g., Kaiser–Meyer–Olkin measure, Bartlett’s test of sphericity), computing a correlation matrix, and extracting factors (common-factor methods such as principal axis factoring or maximum likelihood). Determining the number of factors relies on eigenvalues, scree plots, and sometimes parallel analysis. Rotation (orthogonal like varimax or oblique like oblimin) is applied to achieve a more interpretable factor solution. Outputs consist of factor loadings, communalities, and uniquenesses, with factor scores available for subsequent analyses.

Assumptions include linear relationships among variables and sufficient sample size; ML-based methods assume multivariate normality, though EFA can be robust to deviations. Factor analysis is widely used in psychology, education, and social sciences for construct validation, questionnaire development, and theory testing. It is distinct from principal component analysis, which emphasizes data reduction without separating shared versus unique variance. Factor analysis remains central to modern psychometrics and structural equation modeling, especially in confirmatory contexts.