A question on SEM and path analysis

Question

For my PhD dissertation, I am offering a conceptual model on teacher professional development. My model has one mediator. I wonder if I can test the mediation through Baron and Kenny's procedure or bootstrap and then conduct structural equation modeling (SEM) analysis. Many say the first step (testing mediation) is an extra procedure, and they say SEM will handle mediation analysis. So, how can I justify using both procedures together?

My second question is: should I propose a general research question for my PhD dissertation, such as, "Does $x$ mediate the relationship between exogenous and endogenous variables?" Or should I offer distinct research questions for every path in the model? I really appreciate your insightful responses.

Answer 1

A few thoughts come to mind. I hope they are helpful.

Lets say you have exposure X, outcome Y, and mediator X.

1) Baron and Kenny is, in my opinion, not a very good way to address mediation, at least not without a lot of thougfulness. The main problem is potential "collider bias" REF. If there are confounders of the Z-Y relationship ( Z <-- C --> Y ), these will then act as confounders on the X-Y relationship once you have adjusted for Z, so interpreting the difference in the coefficient for X between models isn't as straightforward as some people make it out to be.

2) Mediation is a fundamentally causal question. Before building your SEM, I would use a Directed Aclylic Graph REF to draw out all of your hypothesized causal relationships. This would include any mediating influence between variables. You should then identify the relationship(s) you are most interested in for your research, and use the DAG to identify potential confounders...inlcuding those of the Z --> Y relationship (given your interest in potential mediation).

3) I would not view your SEM as a collection of linear regressions (though technically that is exactly what it is). The beauty of SEMs is that they are a holistic, theoretical statement about how you think the universe works, that can then be tested against the data. The SEM, like a DAG, should only include what you need to answer your research question. From this perpective, making each relationship in the SEM a "research question" is letting the tail wag the dog. You should have a research question as your starting point, and then build the SEM as appropriate.

Answer 2

Trying different methods seems wise to me for the sake of understanding any differences in the results you receive from different analyses. Baron & Kenny's approach has received a fair amount of criticism (e.g., Pardo & Román, 2013; Hayes, 2009; Zhao, Lynch, & Chen, 2009; Krause et al., 2010), so alternatives to that would seem particularly worth exploring, ideally with attention to the problems that necessitate alternatives. [This may be an incomplete answer to your first question...]

If you are interested theoretically in the mediation question, it makes sense to incorporate it into your introduction and discussion. I would argue that you should have (and communicate) some justification for every path in a model based on prior theory, but in some cases, the question may be simple, such as, "Will variable $a$ predict variable $b$ in roughly the same manner as previous researchers have found?" or, "Will the model fit adequately if I fix this path to one/zero?" Questions like these aren't really interesting so long as the answers are affirmative, so I would only recommend explaining why you're modeling these potentially (even probably, I'd hope) uninteresting paths the way you are (probably to reflect some well-supported theoretical assumption), and discussing any problematic results if they arise. By comparison, a novel question of mediation is probably more interesting regardless of whether the result is problematic: even a "null" result is still a result!