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Structural equation modeling

Structural equation modeling (SEM) is a form of causal modeling that includes a diverse set of mathematical models, computer algorithms, and statistical methods that fit networks of constructs to data. SEM includes confirmatory factor analysis, confirmatory composite 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. Structural equation modeling (SEM) is a form of causal modeling that includes a diverse set of mathematical models, computer algorithms, and statistical methods that fit networks of constructs to data. SEM includes confirmatory factor analysis, confirmatory composite 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 above (top right). In SEM diagrams, latent variables are commonly shown as ovals and observed variables as rectangles. The diagram above 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, and other fields. Criticism of SEM methods often addresses pitfalls in mathematical formulation, weak external validity of some accepted models and philosophical bias inherent to the standard procedures. Structural equation modeling, as the term is currently used in sociology, psychology, and other social sciences evolved from the earlier methods in genetic path modeling of Sewall Wright. Their modern forms came about with computer intensive implementations in the 1960s and 1970s. SEM evolved in three different streams: (1) systems of equation regression methods developed mainly at the Cowles Commission; (2) iterative maximum likelihood algorithms for path analysis developed mainly by Karl Gustav Jöreskog at the Educational Testing Service and subsequently at Uppsala University; and (3) iterative canonical correlation fit algorithms for path analysis also developed at Uppsala University by Hermann Wold. Much of this development occurred at a time that automated computing was offering substantial upgrades over the existing calculator and analogue computing methods available, themselves products of the proliferation of office equipment innovations in the late 20th century. The 2015 text Structural Equation Modeling: From Paths to Networks provides a history of the methods.

[ "Social psychology", "Statistics", "Machine learning", "Developmental psychology", "Marketing", "Most significant antecedent", "OpenMx", "Latent variable path model", "information motivation behavioral", "Partial least squares path modeling" ]
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