This post follows on from Interpreting Results from Multiple Regression, although it isn't necessary to read that post (might just help with the full story). All of the info in this post is taken from the article "Interpreting the Results from Multiple Regression and Structural Equation Models" by Grace and Bollen and wanted to record what I took from it. The figures and a lot of the text is taken straight from this paper.
Structural equation modeling (SEM) helps with some of the issues of multiple regressions. One of the main benefits of SEM is that they let you evaluate model fit in a way that lets you test the model as a hypothesis. You are able to include your own knowledge of the system into your analyses, and come up with more useful hypotheses.
Using the same example as was used in the multiple regression post (mentioned above) where elevation, the age of the plots and fire severity are all variables to help explain the response in plant cover - you can now change the model depending on the relationships among the explanatory variables.
Rather than all three variables having an equal effect on cover like this:
Structural equation modeling (SEM) helps with some of the issues of multiple regressions. One of the main benefits of SEM is that they let you evaluate model fit in a way that lets you test the model as a hypothesis. You are able to include your own knowledge of the system into your analyses, and come up with more useful hypotheses.
Using the same example as was used in the multiple regression post (mentioned above) where elevation, the age of the plots and fire severity are all variables to help explain the response in plant cover - you can now change the model depending on the relationships among the explanatory variables.
Rather than all three variables having an equal effect on cover like this:
You can include logical information in the model, such as fire severity will not influence the age of a plot, so no need to include that relationship, but age could influence fire severity (because of the build up of fuel etc.). In the example used in this paper, their final model looks like this.
In this model, only elevation and fire severity can have a direct impact on plant cover. Elevation can have a direct impact on plant cover, but also an indirect effect of elevation through age and fire severity. Stand age can only affect plant cover through its effect on fire severity.
You should always present both the unstandardized and standardized ceofficients. Both are telling you very different information!