Structural Equations Model (SEM) form Essay ⋆ Political Science Essay Examples ⋆ EssayEmpire

A structural equations model is a representation of a set of relationships among constructs and between those constructs (or latent variables) and their indicators (or observed variables). The first component is the measurement model, which is constituted by the relationships between latent variables (or constructs) and their respective indicators. In contrast to linear regression, which assumes no-measurement error, structural equations modeling (SEM) can model this type of error, and it can be analyzed. The second component is the structural model, which constitutes the set of relationships among latent variables (similar to relationships in linear regression). SEM, which is a second-generation statistical technique, allows for the opportunity to simultaneously test the measurement and structural models (see Figure 1).

Two of the main SEM techniques are covariance-based SEM and partial least squares. Covariance-based SEM, as implemented in LISREL, AMOS, or EQS software, minimizes the differences between the observed and calculated values in the covariance matrix. A formal specification of a structural equations model is given by the following three equations (Bollen, 1989):

η = Bη + Γξ + ζ (structural equation for latent variable model)

Figure 1: A Generic Example Of A Structural Equations Model

Structural Equations Model (SEM) form

x = Λxξ + δ (measurement model—exogenous variables)

y = Λyη + ε (measurement model—endogenous variables)

Where:

η = latent endogenous variables

ξ = latent exogenous variables

ζ = latent errors in equation

B = coefficient matrix for latent endogenous variables

Γ = coefficient matrix for latent exogenous variables

y = observed indicators of η

x = observed indicators of ξ

ε = measurement errors for y

δ = measurement errors for x

Λy = coefficients relating y to η

Λx = coefficients relating x to ξ

A latent variable is a construct not observable or measured directly, but is indirectly measured through observable variables (indicators).The relationships among constructs are sometimes referred to as paths, and the use of path diagrams to graphically depict SEM models is a common practice. In addition, one of the advantages of SEM is the possibility of assessing both direct and indirect effects among constructs.

The adequacy of a covariance-based SEM model can be assessed in two important ways. There are several overall model fit measures, which evaluate the plausibility of the model as a good representation of the actual covariance values that exist among the variables. Some examples are chi-square, adjusted goodness of fit index, goodness of fit index, and normed fit index. Also some specific measures can assess the structural and measurement models. For the measurement model, the size and statistical significance of loadings are the most important ones. For the structural model, the size and statistical significance of path coefficients and the size of the coefficients of determination (R-squares) should be examined.

Bibliography:

Bollen, Kenneth A. Structural Equations with Latent Variables. New York:Wiley, 1989.
Gefen, David, Detmar W. Straub, and Marie-Claud Boudreau. “Structural Equation Modeling and Regression: Guidelines for Research Practice.” Communications of the AIS 4 (2000): 1–80.
Gil-Garcia, J. R. “Using Partial Least Squares in Digital Government Research.” In Handbook of Research on Public Information Technology, edited by G. David Garson and Mehdi Khosrow-Pour, 239–252. Hershey, Penn.: Idea Group, 2008.
Jaccard, James, and Choi K.Wan. LISREL Approaches to Interaction Effects in Multiple Regression. Thousand Oaks, Calif.: Sage, 1996.
Kline, Rex B. Principles and Practice of Structural Equation Modeling. New York: Guilford, 1998.
Maruyama, Geoffrey M. Basics of Structural Equation Modeling. Thousand Oaks, Calif.: Sage, 1998.

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