Mediation analysis and fit indices

[Adrian Li]

Hi all,

I am hoping to run a mediation analysis with covariates. Upon reading old conversations in this channel and the lavaan tutorial, it seems most appropriate to specify covariates in both regressions regarding the mediator ("brain" in this case) and the outcome ("cognition"). The independent variable here is "income".

The syntax as follows:

mediation_model <- '

# mediator

brain ~ a*income + age + sex + ICV + race2 + race3 + head_motion

# direct effect

cognition ~ c*income + b*brain + age + sex + ICV + race2 + race3 + head_motion

# indirect effect (a*b)

ab := a*b

# total effect 

total := c + (a*b)

# proportion mediated

propMed := ab/total*100

`

While I am able to get the coefficients (a, b, c, ab, total, propMed) as expected, the model appears saturated, with CFI = 1 and RMSEA = 0. 

Although I am okay with this, the reviewers are asking to see model fit indices. My question is - is my procedure above correct? If so, does this mean such/all mediation model(s) will be saturated and thus not give fit indices? What would be a recommended next step to respond to reviewers' concerns?

Thank you!

Adrian

Washington University in St. Louis

[Jasper Bogaert]

Hi,

> While I am able to get the coefficients (a, b, c, ab, total, propMed) as expected, the model appears saturated, with CFI = 1 and RMSEA = 0. 

Indeed, the model is saturated because all pathways between the variables are included in your model.

> Although I am okay with this, the reviewers are asking to see model fit indices. 

I think the only way to obtain a model that is not saturated is to exclude the covariates in the regression regarding the mediator (in this case). 

> My question is - is my procedure above correct? If so, does this mean such/all mediation model(s) will be saturated and thus not give fit indices? What would be a recommended next step to respond to reviewers' concerns?

The goal of mediation analyses is to understand the mechanism behind one (or more) effect(s) (-> is it mediated or not). Given that you seem only interested in the effect of income on cognition, I would only specify that indirect effect. I see no reason to include the covariates in the regression regarding the mediator, as in my point of view, they are just confounders that you want to include in your model.

I am not sure whether my suggestions will give you the 'correct procedure'. Perhaps someone with more experience can elaborate on this (and prove me wrong).

Best wishes,

Jasper

Op dinsdag 13 december 2022 om 22:24:14 UTC+1 schreef adrian.zh...@gmail.com:

[Keith Markus]

Adrian,

I may have misunderstood what Jasper wrote.  However, it seems to me that if age is correlated with income and age causes brain (the mediator) then omitting age from the equation for brain could bias the estimate of the causal effect of income on brain, which would then bias the estimate of the indirect effect of income on cognition.  The same goes for other covariates.  So, as long as you are confident than none are common effects of your three central variables, then I think that there is an argument for including them in both equations.  It never hurts to do a sensitivity analysis by running the analysis both ways.

Regarding your original question, I would insert a sentence stating that the model is saturated and fits perfectly and then report the fit indices following that sentence just in case the reviewer/reader still wants to see them.  It is possible for some saturated models (not yours) to fit imperfectly, so it is not completely uninformative.  If they ask you to remove them, then you are back where you started and everyone is on board with that.

Keith

------------------------
Keith A. Markus
John Jay College of Criminal Justice, CUNY
http://jjcweb.jjay.cuny.edu/kmarkus
Frontiers of Test Validity Theory: Measurement, Causation and Meaning.
http://www.routledge.com/books/details/9781841692203/

[Adrian Li]

Thank you both! I have decided to keep the covariates in both models as these covariates could potentially (causally) relate to the mediator and the outcome variable. Thanks you, Keith, for the suggestions!

Adrian

[Jasper Bogaert]

Adrian, Keith,

> I may have misunderstood what Jasper wrote. However, it seems to me that if age is correlated with income and age causes brain (the mediator) then omitting age from the equation for brain could bias the estimate of the causal effect of income on brain, which would then bias the estimate of the indirect effect of income on cognition.  The same goes for other covariates.  So, as long as you are confident than none are common effects of your three central variables, then I think that there is an argument for including them in both equations. It never hurts to do a sensitivity analysis by running the analysis both ways.

I did not think this issue through very well, and I agree with Keith! (Just wanted to add this to make sure nobody gets confused by my earlier answer.)

Op vrijdag 16 december 2022 om 02:22:24 UTC+1 schreef adrian.zh...@gmail.com: