Strukturgleichungsmodellen

Strukturgleichungsmodell (Structural Equation Modeling, SEM) is a multivariate statistical analysis technique that combines factor analysis and path analysis to evaluate complex relationships between observed variables and latent constructs. It enables researchers to specify and test theories about causal relationships among latent variables while accounting for measurement error.

SEM comprises two parts: the measurement model and the structural model. The measurement model links latent constructs to their observed indicators (for example, test items or survey questions) and is a form of confirmatory factor analysis. The structural model specifies the relationships among latent variables, including causality or dependence paths. Some variables are latent (not directly observed) and are inferred from indicators; others may be treated as exogenous observed variables.

Estimation and evaluation: Parameters are estimated from data using methods such as maximum likelihood, robust ML, or partial least squares. Researchers assess model fit with indices such as chi-square, CFI, TLI, RMSEA, and SRMR. A good fit suggests the model reproduces the observed covariance structure, but does not prove causality.

Applications and history: SEM has its roots in the 1960s and 1970s with the development of LISREL by Karl Jöreskog and Dag Sörbom. It has since been implemented in software packages such as LISREL, AMOS, Mplus, and lavaan. It is widely used in psychology, education, sociology, economics, marketing, and other fields to test theories about latent constructs such as ability, attitude, or satisfaction, while explicitly modeling measurement error.

Limitations: SEM requires a well-specified theoretical model and adequate sample size. Results can be sensitive to model misspecification, nonnormal data, and violations of measurement invariance when comparing groups. The approach is descriptive of the data under the assumed model and does not confirm causality without experimental or strong quasi-experimental designs.