Serial Mediation in R with three mediators (and covariates) using Lavaan - How do I code the model?

Question

This is the model I'd like to code. And here's my current lavaan code, but I'm unsure if this is correct. [Note: I'm not interested in the M1*M2 relationship]:

M1 ~ a1*X + covs
M2 ~ a2*X + covs
M3 ~ a3*M1 + a4*M2 + X
Y ~ b*M3 + c*X + covs

IndirectM1 := a1*a3*b
IndirectM2 := a2*a4*b
IndirectM1M2 := (a1*a3*b) + (a2*a4*b)

I'm particularly confused about whether the IndirectM1M2 code is correct. This combined effect of M1, M2 and M3 on Y is of primary interest. I'm also a little confused about whether I need to add the covariates to every path (I think this is correct, as they can reasonably confound the X - M relationships aswell as the M - Y relationships).

Answer 1

For M3, remove the "+ X" since there is no direct effect from X to M3.

The indirect effects for M1 & M2 codes look correct.

The total indirect effect "IndirectM1M2" also looks correct.

For covariates, go with theory. If you think your choice of control variables affect all the paths in this model, then include. I find that a lot of authors think about the covariates in terms of the X-Y relationship and the role these covariates play may not be the same for X-M relationships, but I don't know your research question or variables.

In recent years I have seen several instances of authors running the analyses with and without controls. If the results do not differ much (the exact definition of "much" depends on authors), then they report results without controls and state that results with controls are available upon request. For reference, these were articles published in Journal of Applied Psych and Personnel Psych.