# Structural Equation Modelling (SEM)

Since the advent of computing technology that allows for the easy integration of graphics into documents, a new convention has developed in how path diagrams are constructed. Latent variable names are set off by putting them in ovals. Observed (manifest) variables are set off in rectangles. In complex models, the “boxes” which represent the variables that the researcher has actually measured are combined in groups as a proxy for the latent variable represented by an oval. Thus, the boxes will have arrows that point to one or more ovals.

This convention is closely related to the more advanced technique that grew out of path analysis: Structural Equation Modeling (SEM). Most researchers today think of path analysis as a special case of SEM. This is because SEM can do the same things that path analysis can do, but it goes farther and has fewer restrictions on how researchers can specify models. Perhaps the most important distinction is that path analysis assumes that all of the measured variables are measured without error, with is rather unlikely. SEMs allow the researcher to specifically model error terms using latent variables. This improves the accuracy of the model.

Recall that **latent variables** are variables that are hypothesized to exist by the researcher (and hopefully the rest of the scientific community), but that cannot be directly measured. Take intelligence for example. Intelligence cannot be directly measured, but few would argue that such a construct does not exist. To measure this construct, psychologists use intelligence test scores to stand in as a sort of proxy for the actual variable of interest. Depression is another common example that comes from psychology. You cannot directly measure depression, but you can measure things that are thought to be symptoms of depression. The relationship of this concept to other statistical techniques becomes clearer when we recognize the fact that latent variables can also be called **factors**. This fact gives us a clue that SEM methods are related in purpose to **factor analysis**.

Last Modified: 10/10/2018