Interpreting KHB Indirect Effects With Suppressor Variables?

[Al Adams]

Hi all, I used the KHB user-written command to conduct a mediation analysis.

My code looks something like:

khb reg continuous_var GroupB || M1 M2 M3 , vce(robust)  c($controlvars) disentangle notable

Z-variable	Coef	Std_Err	P_Diff	P_Reduced
GroupB
M1	-8000	1300	60	80.5
M2	-2000	400	50	30.3
M3	4000	2500	-10	-10.8

I would like some help for understanding this output. I have already reading the accompanying Stata Journal article but Kohler et al. (2011), so I understand what each of the columns mean. However, there is no example in there article about interpreting mediators that have different signs.

1. More specifically, assuming no unobserved confounding, the results suggest that the group effect (GroupA vs GroupB) would be reduced by 80.5 percent if the distribution of M1 was equal across groups. Is that an accurate interpretation?

2. Conversely, once again assuming no confounding, the results suggest that the disparity between GroupA and GroupB would increase by 10.8% if we equalized the distribution of M3 between both groups. Is that also an accurate read of the table?

[Al Adams]

Ulrich Kohler If you have a moment, do you mind letting me know if my interpretation is correct? I would greatly appreciate it!

[Ulrich Kohler]

I would agree with your interpretation -- which does not necessarily mean that it is correct. Be aware that terming the variables behind "||" in -khb- to be "mediators" is already an interpretation, or at least indicates that you are using the assumption that M1, M2, M3 are both, causally affected by Group and causally affect the outcome. Building on this assumption, I agree with your interpretation. At the same time, one could also say, that the effect of the groups would decrease by 81% if M1 would not affect the outcome, and that the effect of group would increase by 11 % if M3 would not affect the outcome. It is not possible with -khb- to disentangle these two possible interpretations.

[Al Adams]

Yes, agreed! My interpretation is certainly making causal assumptions. Thank you for your help and word of caution!

[Al Adams]

Prof. Ulrich Kohler

I have two other questions, if I may.

I have not yet seen KHB applied to decompose the effect of interaction terms. I know it is computationally feasible, but are there any limitations in the interpretation or would one interpret the results as one would interpret the results for a parameter of any other single variable?

For example, assuming the results in my initial post were for c.GroupB#c.weight instead of GroupB, would it be correct to say: "The results suggest that the total effect of the interaction between group and weight would be reduced by 80.5 percent if the distribution of M1 was equal across group-weight combinations"?



Would including an interaction now change the interpretation of the decomposition results for the main effect?

In other words, would I still interpret the results for GroupB as I did in my original post? I imagine that one could describe it as the total effect of GroupB that is not due to variation in weight. For instance, would it be accurate to say:

The results suggest that the group effect (GroupA vs GroupB) that is not due to variation in weight would be reduced by 80.5 percent if the distribution of M1 was equal across groups?

As you cautioned and for the sake of simplicity, in my interpretations, I am assuming that GroupB => M1 => outcome (i.e., continuous_var)