Hi Hailey,

first, since mediation is a causal concept, the correctness of the model specification is important. In this regard, how's the fit of this model in terms of the chi-square test? In addition, you should think whether uncorrelated error terms among the errors of the four mediators is reasonable. These imply that A and B explain all the covariances among the mediators (i.e., A and B are the only common causes of two respective mediators). This is often not plausible and leads to misfit which can be avoided. Much more important for the causal interpretation of the indirect effects is the absence of direct effects of A and B and zero error covariances between the mediators and the outcomes. These should be the main target of the model test. If these assumptions hold, then at least the direction of the arrows of the mediator to the outcomes has some support.

Beyond that, use bootstrapping to calculate the standard errors of the indirect effects to address the statistical side of the procedure (beyond the causal-identification side that was aforementioned.)

Don't take any effects or variables out of the model.

HTH

Holger

Hi Hailey,

first, since mediation is a causal concept, the correctness of the model specification is important. In this regard, how's the fit of this model in terms of the chi-square test? In addition, you should think whether uncorrelated error terms among the errors of the four mediators is reasonable. These imply that A and B explain all the covariances among the mediators (i.e., A and B are the only common causes of two respective mediators). This is often not plausible and leads to misfit which can be avoided. Much more important for the causal interpretation of the indirect effects is the absence of direct effects of A and B and zero error covariances between the mediators and the outcomes. These should be the main target of the model test. If these assumptions hold, then at least the direction of the arrows of the mediator to the outcomes has some support.

Beyond that, use bootstrapping to calculate the standard errors of the indirect effects to address the statistical side of the procedure (beyond the causal-identification side that was aforementioned.)

Don't take any effects or variables out of the model.

HTH

Holger

Hi Hailey,

I would go with Holger's recommendation.

Alternatively or additionaly, you could check the 'phantom model approach' by Macho & Ledermann.

Macho, S. and T. Ledermann, 2011, “Estimating, testing and

comparing specific effects in structural equation models: The

phantom model approach”. Psychological Methods, 16: 34–43.

Best, Paul

Holger Steinmetz thank you for the answer. I put covariances among the mediators as well. I have a question. While investigating the mediation from A to G through C, should I delete the paths between A and D, A and E, A and F, C and H?

Hi Hailey,

the model must correspond to your theory. Do you expect effects of these variables? If yes, you have to estimate them. Otherwise the model will not fit and the estimated indirect effects will get biased as the algorithm will try to match the correlation between, say A-G, by biasing the estimating paths.

Best,

Holger