In May of 2020, Dan Bauer and Patrick Curran offered a free three-day Livestream course titled Introduction to Structural Equation Modeling. There were 3,000 participants from 38 countries and six continents. Because many people were unable to register at the time, we are now offering the recordings and materials from this three-day class for just $49 (simply to cover infrastructure costs) within our new online statistics training platform. In the short video below, Dan and Patrick describe the Just-in-Time Introduction to Structural Equation Modeling workshop.
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.