SEM Mediation using bootstrapping approach

[EmmaL]

Hi,

I am performing mediation analysis using structural equation modelling (I'm using the lavaan package in 'R'). I am using the bootstrapping approach (rather than the causal steps approach) and just wanted to clarify two things;

1) My understanding is that using this approach, the the total effect and direct effect does not need to be significant in order for an indirect effect to be significant. So if the bootstrapped confidence intervals do not include zero, then you can state that a significant indirect effect has been found.

However, does the relationship between X->M (a) and M->Y (b) need to be significant?

2) Also, if the confidence intervals are negative (e.g. -.43, -.09), the direct effect is negative (and sig), the beta for (b) is negative (but non-sig) but the beta for (a) is positive (but non-sig), how do you interpret this? The positive relationship for (a) i.e. X->M is throwing me a bit when it comes to writing this up and trying to explain the relationships between the variables!

Thanks in advance!
Emma.

 

[the42up]

what do you mean bootstrapping approach?

Do you mean that you used a bootstrapped covariance matrix?

 

[EmmaL]

I used bias correct bootstrapping to construct a confidence interval (C.I) for the indirect effect of a mediation model?

 

[the42up]

Ok, I am following you now.


May I ask why you chose to use a more contemporary rather than classical approach? The reason I ask this, is that if you plan on submitting, your reviewers will probably ask. In the case of a recent experience, bootstrapping in SEM seems to create a little friction with some more traditional academics. But at least they know what bootstrapping is. On the other hand, causal inference is not on many people's raiders if we are on the same page with the term.

Personally, I like using the bootstrapping method for looking at mediators in an SEM model.

1. you are correct. But be careful here. At times, boot strapping can be a little liberal, ESPECIALLY, a BCA interval. If you have a small-ish sample, this is the approach to use, but if your sample is fine, I recommend a non-bias corrected bootstrap.

2. are you saying that you have a negative direct effect and a positive indirect effect?

Sorry, interpreting SEM models is tricky without a picture (its a terrible crutch for me, but eh, how I learned)

 

[hlsmith]

I enjoyed reading this and yes bootstrap can be used for CI. Can you elaborate on "bias correct bootstrapping", do you just mean you used BS for CI? Because there is an option to bias correct estimates by minus-ing the bootstrap estimate from the calculated estimate, which is different.


I have not really done mediation analysis, but one thing to keep in mind in causality is the "faithfulness assumption", so it is possible to have two paths to the outcome with different signs, which negate each other.