Posted April 1, 2012 by Team AnalyticpediA in Analytics

Structural Equation Modeling:Two Steps Method


The History

Structural equation modelling (SEM) is a collection of statistical procedures that examine the underlying relationships among observed variables. This approach derived from the work of psychometrician Karl Jöreskog and his associates. In the late 1960s and early 1970s, Jöreskog developed a representation for analyzing the structures governing matrices of covariances among observed variables, the “analysis of covariance structures”, commonly referred to as the “LISREL [Linear Structural Relations] Model.” This representation has two components: a measurement component and a structural component. The measurement component reflects relationships between latent variables, constructs, or factors and their manifest indicators or observed variables. It has also been called “confirmatory factor analysis” since it allows for an evaluation of a hypothesized factor solution. The structural component reflects relationships among the latent variables, constructs, or factors themselves. Historically SEM developed from related models: regression, path, confirmatory factor and SEM.

The Concept

Specifically, SEM was developed from a combination of path and factor analysis. Path analysis models allow a study of the structural relationships between observed models. In contrast, Factorial models measures the relationships between survey item responses and underlying theoretical constructs that are not directly modelled. SEM consists of two components- first measurement model and second structural model. In structural modelling, exogenous variables represent those constructs that exert an influence on other constructs under study and are not influenced by other factors in the quantitative model. Those constructs identified as endogenous are affected by exogenous and other endogenous variables in the model. Exogenous, is similar to independent variables and endogenous, similar to dependent or outcome variables. Exogenous and endogenous variables can be observed or unobserved, depending on the model being tested. The measurement model of SEM depicts the pattern of observed variables for those latent constructs in the hypothesized model. A major component of a CFA is the test of the reliability of the observed variables. Measurement model is also used for examining the interrelationships and covariation among the latent constructs. As part of the process, factor loadings, unique variances, and modification indexes are estimated for one to derive the best indicators of latent variables prior to testing a structural model. The structural model comprises the other component in linear structural modelling. The structural model displays the interrelations among latent constructs and observable variables in the proposed model as a succession of structural equations—akin to running several regression equations. Structural equation models (SEMs) explain the relationships between variables. They are combinations of multiple regression and factor analysis. SEM provides handful of competitive advantage over these techniques in terms of dealing with multi collinearity and unreliability of the data set.

The Advantages

Unlike SEM which can help analysing more than one relationship at same time, regression analysis permits to look at only one equation at a time. Since in the real life scenario no factor exists alone, using SEM is more pragmatic. This method takes potential measurement errors into account, which regression is incapable of doing. SEM is an advance tool when compared to Factor Analysis and regression analysis. Structural equation modelling (SEM) grows takes into account the modelling of interactions, nonlinearities, correlated independents, measurement error, correlated error terms, multiple latent independents. SEM could be useful substitute for multiple regression, path analysis, factor analysis, time series analysis, and analysis of covariance. The maturation of SEM over the last 30 years now allows for analysis of more advanced models. Multi-level modelling is now possible. For example, educators or policy makers interested in regional, school-level, teacher and student data can now model the inter-relationships between these variables through multi-level modelling. Finally, SEM software programs have changed significantly from the early versions in which researchers used matrix and Greek notation to input program syntax. Now, more user-friendly windows-based programs with pull-down menus and drawing programs which input syntax are available. A SEM analysis involves the solving of a series of simultaneous regression equations.

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