In an earlier section, we mentioned that to ultimately find a good solution, software has to use trial and error to come up with an implied covariance matrix that matches the observed covariance matrix as well as possible. The question is what does "as well as possible" mean? The answer to this is that the software must try to minimize some particular criterion, usually some sort of discrepancy function. Just what that criterion is depends on the estimation method used. The most commonly used estimation methods in SEM include:

There are a number of other estimation methods as well, some of which can be done in R, but here we will stick with describing the most common ones. In general, OLS is the simplest and computationally cheapest estimation method. GLS is computationally more demanding, and ML is computationally more intensive....