Hi,
The short version of this question is whether it is feasible to test mediation by adding triple interaction terms with continuous mediator variables.
I'm in the middle of designing a "channel study" that intend to split direct & indirect effects of the treatment effect I found in my last project. In that project, I applied standard DiD approach with i.POST##i.Treatment.
Before conducting a standard path analysis/SEM. Now I'm thinking, if it's possible to reuse my previous work; and extend/modify the DiD setting to somehow test effects of hypothesized mediators. The general model in my mind is something like:
reg Y i.POST##i.Treatment i.POST##i.Treatment##c.Mediator1 i.POST##i.Treatment##c.Mediator2.......... i.IndFixedEffect i.YearFixedEffect
So the estimated coefficients on triple interactions (post x treatment x continuous mediator variable: X1,X2...) can be interpreted as the extent of treatment affect Y via moderating of X1 X2 etc.
I can not find any reference that specific to this approach other than Acemoglu, Autor and Lyle (2004) interpret the interaction with continuous variable as "intensity of treatment". While it is obviously not the same as what's in my mind. There are various concerns such as dilution of "main/direct effect"; offset each other etc. And my gut feeling is that it is very difficult, if not impossible, to simplify what essentially a path analysis into one regression; meanwhile got a set of comparable effects. However, I do not have the ability to convince myself the model above won't work, to any extent, either.
Please anyone can help me to determine if this would work and what coefs on triple interactions mean?
Thanks in advance,
Will
The short version of this question is whether it is feasible to test mediation by adding triple interaction terms with continuous mediator variables.
I'm in the middle of designing a "channel study" that intend to split direct & indirect effects of the treatment effect I found in my last project. In that project, I applied standard DiD approach with i.POST##i.Treatment.
Before conducting a standard path analysis/SEM. Now I'm thinking, if it's possible to reuse my previous work; and extend/modify the DiD setting to somehow test effects of hypothesized mediators. The general model in my mind is something like:
reg Y i.POST##i.Treatment i.POST##i.Treatment##c.Mediator1 i.POST##i.Treatment##c.Mediator2.......... i.IndFixedEffect i.YearFixedEffect
So the estimated coefficients on triple interactions (post x treatment x continuous mediator variable: X1,X2...) can be interpreted as the extent of treatment affect Y via moderating of X1 X2 etc.
I can not find any reference that specific to this approach other than Acemoglu, Autor and Lyle (2004) interpret the interaction with continuous variable as "intensity of treatment". While it is obviously not the same as what's in my mind. There are various concerns such as dilution of "main/direct effect"; offset each other etc. And my gut feeling is that it is very difficult, if not impossible, to simplify what essentially a path analysis into one regression; meanwhile got a set of comparable effects. However, I do not have the ability to convince myself the model above won't work, to any extent, either.
Please anyone can help me to determine if this would work and what coefs on triple interactions mean?
Thanks in advance,
Will