The basic ideas of SEM

In the previous chapter, we went over the concepts of path coefficients and covariance algebra. In reality, these terms, though used for exploratory factor analysis, come from the tradition of SEM. Exploratory factor analysis (EFA) simply attempted to model covariance structure based on identifying common sources of variance. Alternatively, SEM attempts to use covariance to model many, very explicit relationships between variables. Like EFA, SEM can incorporate both observed and unobserved variables, but unlike EFA, SEM does not necessarily need to have unobserved variables. In SEM, the relationships between variables can be represented as a series of paths, whether those variables are observed or latent. The correlation between any two variables is a path coefficient. Each observed variable will also have some residual correlation, and residual correlations may be correlated with one another, something that is not allowed in EFA.

Components of an SEM model

The following...