Estimating indirect effects using xtdpdml for SEM

[Felicitas Koch]

Hello,

I am currently looking for some guidance regarding how to correctly estimate indirect effects using the xtdpdml shell for SEM. I have panel data on the country level for t=5, thus requiring the xtdpdml command.

Assuming a simplified example from my research question, the regression using SEM would look somewhat like this. rch_nrg is Y, grwth_epriceres_cent is M and grwth_metalseur is the explanatory variable X.

 sem (grwth_epriceres_cent -> rch_nrg, ) (grwth_metalseur -> rch_nrg, ) (grwth_metalseur -> grwth_epriceres_cent, ), nocapslatent

From what I've read from the work of Richard Williams, Paul D. Allison and Enrique Moral-Benito as well as other entries in the forum, I cannot use the standard SEM command given that I deal with panel data. Thus, I am using the xtdpdml command. Similar to the SEM code above, I've run the code

xtset countryID timeID
xtdpdml rch_nrg grwth_epriceres_cent grwth_metalseur, ylag(1) tsoff tfix vce(oim) difficult showcmd

This then gives me the following SEM code:

sem (rch_nrg2 <- rch_nrg1@b1 grwth_epriceres_cent2@b2 grwth_metalseur2@b3 Alpha@1 ) (rch_nrg3 <- rch_nrg2@b1 grwth_epriceres_cent3@b2 grwth_metalseur3@b3 Alpha@1 ) (rch_nrg4 <- rch_nrg3@b1 grwth_epriceres_cent4@b2 grwth_metalseur4@b3 Alpha@1 ) (rch_nrg5 <- rch_nrg4@b1 grwth_epriceres_cent5@b2 grwth_metalseur5@b3 Alpha@1 ) (rch_nrg6 <- rch_nrg5@b1 grwth_epriceres_cent6@b2 grwth_metalseur6@b3 Alpha@1 ), var(Alpha) difficult iterate(250) technique(nr 25 bhhh 25) noxconditional vce(oim)

However, despite the general information available on this command, it is not clear to me how estimate the indirect effect. Based on my understanding of SEM and xtdpdml, this only gives me the direct effect of both my X and M variable on Y. Would estimating the indirect effect, similar to the first code of SEM, then require me to "manually" insert the code for estimating X on M into the code above? Something along the lines of:

sem (rch_nrg2 <- rch_nrg1@b1 grwth_epriceres_cent2@b2 grwth_metalseur2@b3 Alpha@1 ) (rch_nrg3 <- rch_nrg2@b1 grwth_epriceres_cent3@b2 grwth_metalseur3@b3 Alpha@1 ) (rch_nrg4 <- rch_nrg3@b1 grwth_epriceres_cent4@b2 grwth_metalseur4@b3 Alpha@1 ) (rch_nrg5 <- rch_nrg4@b1 grwth_epriceres_cent5@b2 grwth_metalseur5@b3 Alpha@1 ) (grwth_epriceres_cent <- grwth_metalseur2@b1 Alpha@1 ) (grwth_epriceres_cent <- grwth_metalseur3@b1 Alpha@1 ) (grwth_epriceres_cent <- grwth_metalseur4@b1 Alpha@1 ) (grwth_epriceres_cent <- grwth_metalseur5@b1 Alpha@1 ), var(Alpha) difficult iterate(250) technique(nr 25 bhhh 25) noxconditional vce(robust)

Does this make sense or is there another way estimating the indirect effect using the xtdpdml command that I have not (yet) come across?
Thank you very much in advance!

[Richard Williams]

If you use the staywide option, you should be able to use sem's post-estimation commands, including estat teffects. estat teffects reports direct, indirect, and total effects for each path (Sobel 1987), along with standard errors obtained by the delta method. Something like

use https://www3.nd.edu/~rwilliam/statafiles/wages, clear
xtset id t
xtdpdml wks L.lwage, inv(ed) pre(L.union) ti(Baseline Model) show staywide
estat teffects

Making sense of it all may be harder than usual because of the multiple time periods.

[Felicitas Koch]

Thank you a lot, this helped!