Mediation with KHB and GSEM in the case of a binary mediator

[Lydia Palumbo]

Dear Stata Users,

I used a mediation analysis through KHB method for a linear regression with the following specification:

 . khb reg futrj ib1.nssec3 || i.mfamily314

Decomposition using Linear Probability Models

Model-Type:  regress                               Number of obs     =   11083
Variables of Interest: ib1.nssec3                  R-squared         =    0.03
Z-variable(s): i.mfamily314
 
                     
futrj    Coef.   Std. Err.    z    P>z    [95% Conf.    Interval]
                    
0.nssec3    
Reduced    6.695983   .5852068    11.44    0.000    5.548998    7.842967
Full       7.826557   .5912519    13.24    0.000    6.667724    8.985389
Diff      -1.130574    .112541    -10.05    0.000    -1.351151    -.9099979
                    
1.nssec3    (base outcome)
                    

with a confounding ratio amounting to -16.88.

I want to check whether I was able to find the same results through the Baron and Kenny method via GSEM. You can find the path diagram below






Since mfamily314 (mediator) is a binary variable, I am not sure whether I need to specify a Gaussian link or a Multinomial link (in that case the specification would be 1.family314).

From my results, the specification that gives the same results as the KHB method is the one with a Gaussian link.

However, I was wondering whether this specification is theoretically correct due to the categorical nature of the mediator.

Thank you very much and best regards,
Lydia

[Lydia Palumbo]

This is the path

[Tom Scott]

I don't think either are a great sensitivity check. Treating the binary mediator as normally distributed brings its own issues (your third approach), and so does comparing a logistic coefficient to another regression coefficient (your second approach). Although I think simulation studies have shown OLS regression is pretty robust to violations of normality, I still don't think it is appropriate to treat any correspondence between your khb results and your findings from the latter approach as support for your khb findings. I would go with the khb approach and explain why it is a better approach than your latter two approaches for the reasons discussed in the khb author articles.

[Max Coleman]

Perhaps I'm missing something, but I'm not sure I understand why you would use a multinomial link. Wouldn't you want to use logit since the mediator is binary?

Also: if the one that's identical to KHB uses a gaussian link, doesn't that essentially mean that Stata is treating this as an OLS regression (in which case KHB would be unnecessary)?

[Lydia Palumbo]

Hi,

thank you both for your answers.

Yes, I could use a logit but, when I specifiy the logit link, I cannot express the variable as categorical. Therefore, the path (M-->Y) is estimated through an OLS treating M as continuous.
I was able to consider M as categorical only by using a multinomial link. However, after posting this thread, I found out that this is just a limitation of the graphical path. If I specify the gsem path
through command-language notation, I would't need to specify a multinomial link.

With regard to the second question, I was questioned to try the B&K mediation instead of KHB, because the KHB would not be necessary with OLS (as you said). However, I have this doubt about
the binary mediator, as I am not sure whether it is correct to specify an OLS link to estimate the path X-->M (instead of a logit/multinomial). A thread that I found to be quite close to my question is the
following.
https://www.statalist.org/forums/for...ical-mediators
From my understanding, I would need to specify the link of the dependent variable.

Hope this clarifies my previous posts.

Thank you very much again.

[Tom Scott]

The logit link function is for your dependent variable. It has nothing to do with your independent variable. If M is a binary variable, you should use a logistic/probit regression to regress M on X. If Y is continuous and normally distributed, you should use an OLS regression to regress Y on M. Because you cannot compare logit regression coefficients (first equation) to OLS regression coefficients (second equation), you cannot use traditional methods of mediation where you compare the regression coefficients. Therefore, you should use the khb method to estimate the indirect effect of X on Y through M. I suggest reading Paul Allison "comparing Logit and Probit Coefficients across groups" and "total, direct, and indirect effects in logit and probit models" by Breen, Karlson, and Holm.

[Lydia Palumbo]

Thank you. I found what I needed in the Breen, Karlson, and Holm's paper (pp.174-175).