In this edition of CBA Office Hours, Dan discusses some of the principal advantages of the structural equation model (SEM) relative to more traditional data analytic approaches like the linear regression model. Advantages include the ability to account for measurement error when estimating effects, test the fit of the model to the data, and specify statistical models that more closely align with theory. Dan describes these advantages with an example on factors that relate to children’s popularity with peers. We consider these issues and various extensions of the SEM (such as longitudinal applications, ways of formally testing mediation and moderation, and evaluating invariance of effects across groups both known and unobserved) in greater detail in other posts on SEM and in our summer training workshops.
An equivalent model can be thought of as a re-parameterization of the original model. In other words, it is just a different way of “packaging” the same information in the data and no equivalent model can be distinguished from another based on fit alone. If you were to fit a series of equivalent models to the same sample data you obtain exactly the same chi-square test statistic, RMSEA, CFI, TLI, and any other omnibus measure of fit. It is often best to treat this as a limitation of any given study and to potentially present one or a small number of equivalent model options to the reader so that these too might be considered as plausible representations of the data.