Different types of mediation analysis I'm completing a systematic review and one of my inclusion criteria is the study must have conducted a formal mediation analysis. I'm struggling to find any papers or books that list all the possible ways in which one can test for mediation. Do you know of any references of such? Or know a list of all possible ways to test for mediation? 
Thanks!
 A: I have faced similar issues as well. I do not believe any such list will be exhaustive. For your literature review, it may be overly restrictive to formally name the test(s) of mediation applied. At the very least, you will also need to critically review all the excluded articles. Some of the language around such tests can be quite vague as I'll describe below.
Basically, there are two commonly estimated mediation effects: the Baron and Kenny approach and path analysis. Path analysis is also often called structural equation modeling, and there are a few other names as well. Baron and Kenny's approach estimates an indirect effect using two regression models whereas path models estimate the indirect effect in a single conditional path model. The hypothesis tests for these effects (either in a path model or with BK) can be produced by bootstrapping, permutation testing, or using model based inference. In fact the original approach from B&K suggested using a model based approach with some approximate SE estimates. Later researchers proposed better SE estimates but still attributed the effect to B&K.
What I often find is that authors just describe these components and say they will do a mediation analysis. There is no formal name for the tests because mediation is just a covariate(s) in a regression model(s). For instance, here we see extensive discussion about using permutation tests to test for mediation, but as far as I can see, the author has resolved to use either the B&K measure or the path model measure, and "permutation" is just a means of calculating a p-value as you would do for a mean difference in a t-test. Sadly, "permutation tests" are now attributed to testing for mediation. But permutation tests can test for practically anything, and I don't expect clear language to indicate "we performed a permutation test of mediation" consistently.
That's perhaps the best way to think about it: think of the indirect effect of mediation like a mean difference, an association measure, and the tests thereof are just tests of model effects. That may explain why there really isn't a formal name for the tests.
