Hi all,
I am studying the effect of child health on educational outcomes. My IV is the likelihood of attending an upper secondary school track (vs. lower track) in T2 and my DV of interest is health status in T1 (very/good health vs. fair/poor health). I use a lagged variable logistic regression approach.

I would now like to decompose the effect of family background (tertiary education vs. lower) in order to analyze the contribution of child health in relation to the contribution of other factors, such as GPA (T1), while controlling for various other variables such as age, gender, etc.

Following the assumption that health problems reduce the likelihood of upper secondary school attendance (confirmed in prior analysis), my hypothesis is that health problems are a mediator of family background on gymnasium attendance, as health problems (1) occur more often in families with non-tertiary education (confirmed in prior analysis) and (2) have a stronger negative effect on the likelihood of gymnasium attendance in families with non-tertiary education than in families with tertiary education (confirmed in prior analysis). I am now interested in quantifying the contribution of health problems in the overall effect of family background.

I have performed a KHB decomposition:

Code:
khb logit schooltrack family_tertiary || healthproblems gpa, concomitant($control_vars) disentangle
However, this procedure was criticized for not taking into account the interaction effect of the second part of my hypothesis: (2) family background#health problems. I was advised to use an Oaxaca/Blinder decomposition instead. However, as far as I know, this method does not allow me to analyze the contribution of single variables, such as health problems and GPA, but gives me the overall contribution of endowments and coefficients (in the threefold version).

Does anyone have a suggestion on how to model this decomposition? Is it possible to just include the interaction in the KHB model?

Many thanks in advance and sorry for the long text!

Best,
Lisa