Structural equation modeling

The term structural equation model indicated a statistical technique for testing and estimating correlative relationships between endogenous variables and exogenous variables as well as the hidden structures between. It can be verified whether the hypothesis assumed before the application of the method correspond to the given variable. It is attributed to the structure under test multivariate methods and has a confirmatory ( confirmatory ) character. Approaches to structural equation modeling can be fundamentally different in covarianzbasierte and variance based ( partial least squares, PLS ) method, which have similarities and differences.

Structural equation models play an important role, among others in empirical social research. A special feature of structural equation models is checking latent (not directly observable ) variables. Path analysis, factor analysis and regression analysis can be viewed as special cases of structural equation models. A structural equation model is in turn a special case of a causal model dar.

Model elements

• Indicator ( Item): This is observed variables. For example, indicators of "intelligence" of the " final mark in the Abitur ", the " intelligence quotient " and the "number of languages ​​covered by one person ". Usually, the use of at least four indicators is recommended in the model.
• Latent variable (factor): This is the unobserved variable that is only measured by their indicators. In the example " intelligence" the latent variable. A distinction is made between independent variables latent ( = exogenous ) and dependent latent ( = endogenous ).
• Measurement model ( measurement model): this is the core of the structural equation model. In him the sense of a confirmatory factor analysis ( confirmatory factor analysis) connections between the indicators and the latent variables modeled. Here, the covariance plays a crucial role.
• Structural model ( structural model): This is the amount of exogenous and endogenous variables and their compounds.

Modeling

For modeling Mulaik and Millsap (2000) have suggested four steps. In the first step, a factor analysis is performed to determine the number of latent variables. Using a confirmatory factor analysis of the measurement model is confirmed in the second step. In the third step, the structural model is tested. In the fourth step nested models are tested to identify the most economical.

However, it should be noted that a warning in the literature before, to modify models as long until they "fit". Rather, always a new sample must be collected for testing modified or new hypotheses.

Software

For the creation of structural equation models, the software packages LISREL, AMOS and EQS have been established, which serves as an extension of SPSS AMOS. AMOS is considered to be more user friendly than the older, but still established LISREL.

The statistical software R supports the creation of structural equation modeling with the packages ' lavaan ', ' openmx ' and ' this '.

The freely available Ωnyx provides a graphical interface for modeling and supports the export of the model according to openmx and Mplus.

The command line- based software Mplus Muthen & Muthen of explicitly allows for the inclusion of weighting factors, as used for example in the context of panel surveys.

Furthermore, software packages are offered based on the partial least squares method (PLS ) method based on how SmartPLS, PLSGraph, ProPLS.