# Structural Equation Modeling Structural equation modeling (SEM) is a particular form of data analysis. According to this approach, a researcher begins with a model that specifies how multiple variables are related to each other. These theorized relationships are formalized into a set of equations that include the variables in question. These variables are then measured and their relations to each other are quantified. The test of the model involves an assessment of how well the equations can reproduce or “fit” the observed relations.

As a simple example, consider a model in which the researcher theorizes that variable A influences C because of its influence on B. Schematically, A — B — C. This model has two equations, one that predicts B using A and one that predicts C using B. To test this model, the researcher measures the observed relations between A, B, and C. Application of SEM provides tests of (1) whether A is actually a useful predictor of B, (2) whether B is actually a useful predictor of C, and (3) whether the model as a whole fits the observed data. The latter test is not simply redundant with the previous two tests. The reason for this is that the model specifies that A is only a predictor of C because of its relation to B. A might be a useful predictor of B, and B of C, but the model might provide a poor fit because the researcher has incorrectly specified that A has no direct relation with C.

As can be seen, the proper use of SEM requires that the researcher has carefully thought about the ways variables are related to each other before collecting the data. In this sense, application of SEM is typically considered to be confirmatory in nature rather than exploratory. Although researchers often conceptualize the associations among variables in terms of causal influences, causality cannot be inferred simply from observed relations (the term causal modeling is therefore a misnomer). Once a relation has been identified and placed in the context of a larger set of variables using SEM, researchers are best advised to test for causality using experimental designs.

As might be imagined, SEM can be an extremely powerful and flexible data analytic technique. Indeed, many other data analytic strategies can be thought of as specific forms of SEM, including linear and nonlinear regression, path analysis, factor analysis, and hierarchical modeling. SEM actually allows the researcher to combine several of these simpler data analytic techniques in a single analysis rather than conducting separate analyses using multiple steps. For example, one of the more popular applications of SEM involves a combination of factor analysis and path analysis. Because factor analysis deals with latent, or unobserved, variables, this form of analysis is often referred to as latent variable modeling.

As might be expected, most application of SEM are computationally complex and require sophisticated statistical computer packages. Among the most popular of these is LISREL.

### References:

1. Bollen, K. A. (1989). Structural equations with latent variables. New York: Wiley.
2. Kline, R. B. (2004). Principles and practice of structural equation modeling (2nd ed.). New York: Guilford Press.
3. McDonald, R., & Ho, M. R. (2002). Principles and practice in reporting structural equation analyses. Psychological Methods, 7, 64-82.
4. Raykov, T., & Marcoulides, G. A. (2006). A first course in structural equation modeling. Mahwah, NJ: Erlbaum.