Structural Equation Modeling

Structural equation modeling (SEM) is a statistical technique for testing and estimating causal relations using a combination of statistical data and qualitative causal assumptions. This definition of SEM was articulated by the geneticist Sewall Wright (1921), the economist Trygve Haavelmo (1943) and the cognitive scientist Herbert A. Simon (1953), and formally defined byJudea Pearl (2000) using a calculus of counterfactuals.

Structural Equation Models (SEM) allows both confirmatory and exploratory modeling, meaning they are suited to both theory testing and theory development. Confirmatory modeling usually starts out with a hypothesis that gets represented in a causal model. The concepts used in the model must then be operationalized to allow testing of the relationships between the concepts in the model. The model is tested against the obtained measurement data to determine how well the model fits the data. The causal assumptions embedded in the model often have falsifiable implications which can be tested against the data.  

Equivalent Models

In SEM, many models are equivalent in that they predict the same mean vector and covariance matrix. A "cleaned" model representation would be to model the mean and covariance matrix directly. That is, a "Clean Normal Model" (CNM) is a model with a function for every entry of the covariance matrix and mean. In terms of path diagrams, CNM is the subset of SEMs that only have squares connected by double-headed edges. CNMs are not popular for at least two reasons:

• CNMs are very difficult for human readers to interpret. Humans typically like to think of covariances as common sources or causations. It helps people to think of models, even though it also entails the danger of over-interpreting regressions as causations. Note that this mere re-representation had big successes: The IQ index, for example, although by definition not existent in the real world, has arguably the greatest success in Psychology, with lots of predictive power for many things.

• It helps us to integrate variables that we propose do exist, but have not been measured (yet). We could for example build a model in which ion flow in certain brain cells is a latent variable and in that way make a prediction about the covariance of the ion flow to observable variables, which, if someone invents a measurement instrument that allows the measurement of this flow in the specific region, can be falsified or confirmed.

Advanced uses

• Invariance 

• Multiple group modelling: This is a technique allowing joint estimation of multiple          models, each with different sub-groups. Applications include behavior genetics, and analysis of differences between groups (e.g., gender, cultures, test forms written in different languages, etc.).

• Latent growth modeling
• Hierarchical/multilevel models; item response theory models
• Mixture model (latent class) SEM
• Alternative estimation and testing techniques
• Robust inference
• Survey sampling analyses
• Multi-method multi-trait models
• Structural Equation Model Trees

Source: http://en.wikipedia.org/wiki/Structural_equation_modeling

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