Is gsem appropriate for a parallel two-mediator model with a binary IV and two binary mediators?

[Tongtong Li]

Dear Statalist members,

I would like to confirm whether gsem is a suitable approach for the following mediation setup.

I have a binary independent variable (X), two binary mediators (M1 and M2) operating in parallel, and two outcomes that I analyse separately: one continuous outcome, and one unordered categorical outcome with four levels.

For the continuous outcome, I specified the model as follows:

gsem (m1 <- i.x, logit) (m2 <- i.x, logit) (y <- i.m1 i.m2 i.x)

and computed the specific indirect effects as products of the a- and b-path coefficients using nlcom, with bootstrap confidence intervals.

My questions:

1. Is gsem with nlcom/bootstrap an appropriate way to estimate the indirect effects here, given the binary mediators?
2. For the four-category unordered outcome, would gsem with an mlogit outcome still be appropriate, and how are indirect effects best defined and reported in that case? Or would another command be more suitable?

I am using Stata 17. Thank you for your help.

[smith Jason]

Your model for the continuous outcome is, in my opinion, a reasonable and commonly used application of gsem. Estimating the binary mediators with logistic links and the continuous outcome with a linear model, then obtaining the specific indirect effects as products of the corresponding path coefficients using nlcom with bootstrap confidence intervals, is a standard workflow in Stata.

The main caveat is interpretational rather than computational. With binary mediators, the a paths are log-odds coefficients, so the product-of-coefficients approach does not have exactly the same interpretation as in a purely linear SEM. Nevertheless, this approach is widely used when fitting generalized SEMs.

I would be more cautious about the multinomial outcome. While gsem can certainly estimate a multinomial logit outcome, there is no built-in analogue of estat teffects for gsem, and indirect effects are no longer uniquely defined. A multinomial logit model estimates separate equations for each non-reference category, so any product-of-coefficients calculation becomes category-specific rather than representing a single overall indirect effect.

Therefore, my view would be:

• For the continuous outcome, your gsem + nlcom + bootstrap approach is appropriate and defensible.
• For the multinomial outcome, I would avoid simply reporting products of coefficients as "the" indirect effects without further justification. If the goal is causal mediation, a counterfactual framework (natural direct and indirect effects) or probability-based decomposition would generally provide a clearer interpretation than category-specific coefficient products.

[Tongtong Li]

Your model for the continuous outcome is, in my opinion, a reasonable and commonly used application of gsem. Estimating the binary mediators with logistic links and the continuous outcome with a linear model, then obtaining the specific indirect effects as products of the corresponding path coefficients using nlcom with bootstrap confidence intervals, is a standard workflow in Stata.

The main caveat is interpretational rather than computational. With binary mediators, the a paths are log-odds coefficients, so the product-of-coefficients approach does not have exactly the same interpretation as in a purely linear SEM. Nevertheless, this approach is widely used when fitting generalized SEMs.

I would be more cautious about the multinomial outcome. While gsem can certainly estimate a multinomial logit outcome, there is no built-in analogue of estat teffects for gsem, and indirect effects are no longer uniquely defined. A multinomial logit model estimates separate equations for each non-reference category, so any product-of-coefficients calculation becomes category-specific rather than representing a single overall indirect effect.

Therefore, my view would be:

• For the continuous outcome, your gsem + nlcom + bootstrap approach is appropriate and defensible.
• For the multinomial outcome, I would avoid simply reporting products of coefficients as "the" indirect effects without further justification. If the goal is causal mediation, a counterfactual framework (natural direct and indirect effects) or probability-based decomposition would generally provide a clearer interpretation than category-specific coefficient products.

Jason,

Thank you so much for your thoughtful suggestions! They've been really helpful. If you don't mind, I have a few follow-up questions I'd be very grateful for your thoughts on:

1. For the continuous outcome, I understand the coefficient products aren't on a fully consistent scale. When interpreting the indirect effects here, is there anything in particular you'd suggest I be careful about?

2. Regarding a counterfactual decomposition, I've found it a bit difficult to implement in Stata for my design. The counterfactual commands (`paramed`, `med4way`, `mediate`) seem to handle only one mediator at a time, so a genuine parallel two-mediator model doesn't appear straightforward. I wanted to check whether that matches your understanding, or whether there's an approach I might be missing.

3. Finally, I was wondering whether a stepwise approach (estimating each path separately and testing whether the coefficients are significant) would be considerably more convenient here. I'd really value your view on whether that's a reasonable route.

Thank you again for taking the time.