# Structural Equation Modeling (SEM) Algorithm

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A Structural Equation Modeling (SEM) Algorithm is a modeling algorithm for estimating causal relations using a combination of statistical data and qualitative causal assumptions.

## References

### 2017

- (Wikipedia, 2017) ⇒ https://en.wikipedia.org/wiki/Structural_equation_modeling Retrieved:2017-11-10.
**Structural equation modeling**(**SEM**) includes a diverse set of mathematical models, computer algorithms, and statistical methods that fit networks of constructs to data.SEM includes confirmatory factor analysis, path analysis, partial least squares path modeling, and latent growth modeling. The concept should not be confused with the related concept of structural models in econometrics, nor with structural models in economics. Structural equation models are often used to assess unobservable 'latent' constructs. They often invoke a measurement model that defines latent variables using one or more observed variables, and a structural model that imputes relationships between latent variables. The links between constructs of a structural equation model may be estimated with independent regression equations or through more involved approaches such as those employed in LISREL.Use of SEM is commonly justified in the social sciences because of its ability to impute relationships between unobserved constructs (latent variables) from observable variables. To provide a simple example, the concept of human intelligence cannot be measured directly as one could measure height or weight. Instead, psychologists develop a hypothesis of intelligence and write measurement instruments with items (questions) designed to measure intelligence according to their hypothesis. They would then use SEM to test their hypothesis using data gathered from people who took their intelligence test. With SEM, "intelligence" would be the latent variable and the test items would be the observed variables. A simplistic model suggesting that intelligence (as measured by four questions) can predict academic performance (as measured by SAT, ACT, and high school GPA) is shown below. In SEM diagrams, latent variables are commonly shown as ovals and observed variables as rectangles. The following diagram shows how error (e) influences each intelligence question and the SAT, ACT, and GPA scores, but does not influence the latent variables. SEM provides numerical estimates for each of the parameters (arrows) in the model to indicate the strength of the relationships. Thus, in addition to testing the overall theory, SEM therefore allows the researcher to diagnose which observed variables are good indicators of the latent variables.Various methods in structural equation modeling have been used in the sciences, business, education, and other fields. Use of SEM methods in analysis is controversialbecause SEM methods generally lack widely accepted goodness-of-fit statisticsand most SEM software offers little latitude for error analysis. This puts SEM at a disadvantage with respect to systems of regression equation methods, though the latter are limited in their ability to fit unobserved 'latent' constructs.

### 2005

- (Kline, 2005) ⇒ Rex B. Kline. (2005). “Principles and Practice of Structural Equation Modeling (2nd edition)." Guilford Press. ISBN:1593850751

### 2000

- (Gefen et al., 2000) ⇒ David Gefen, Detmar W. Straub, and Marie-Claude Boudreau. (2000). “Structural Equation Modeling and Regression: guidelines for research practice.” In: Communications of Information Systems, 4(7).