Nonlinear decomposition with interaction effect

[Lisa Muller]

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:

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

[ericmelse]

Dear Lisa,

Possibly, this paper, just published, might be of use to you:

Smith, E. K., Lacy, M. G., & Mayer, A. (2019). Performance simulations for categorical mediation: Analyzing khb estimates of mediation in ordinal regression models. The Stata Journal, 19(4), 913–930. https://doi.org/10.1177/1536867X19893638

Best,
Eric

[Franci Taale]

I will be grateful if you could advance my understanding of the double hurdle model in relation to how to estimate the elasticities of explanatory variables the marginal effects of explanatory variables can be used to calculate elasticities for the probability of a positive expenditure, the conditional level of expenditure and the unconditional level of expenditure. Upon reading John Eakins’ (2016) work: An Application of the double hurdle model to petrol and diesel household expenditure in Ireland, it was fairly easy for me to decide on the appropriate specification for my dataset. However, I am unable to estimate the elasticities and is soliciting support. Any written commands will be deeply appreciated. I can send my data and dofile, if they are needed. Thanks.

[ericmelse]

Dear Franci,

Possibly some other Statalister can help you out on #3. I am not familiar with double hurdle models.

Eric

[Franci Taale]

thank you. i am hoping that someone will finally offer help

[Carlo Lazzaro]

Franci:
an international acknowledged expert on that kind of models (althoug mainly in health economics/health econmetrics) and pretty regular contributor to Stata forum is John Mullahy.
Look for his replies in this forum and, extensively, for his publications.

[Lisa Muller]

Dear Eric,
many thanks for the paper! However, I found that it does not really adress my specific problem. Does anyone have further ideas on this matter? I would appreciate your help very much!

Is it meaningful to include an iteraction with the key independent variable when you want to decompose its effect? I am thinking of something like

 
 khb logit schooltrack family_tertiary || gpa healthproblems family_tertiary#healthproblems, concomitant($control_vars) disentangle

Many thanks,
Lisa

[Franci Taale]

many thanks, Lazzaro. I will follow up and send him an email to that effect.

[Carlo Lazzaro]

Franci:
my advice did not imply to send and email to John Mullahy (as contacting forum members privately for matters related to statistics or queries posted on this forum is highly deprecated - see the FAQ) but to skim through the forum in search of John's replies and (even better) googling in search of his publications (suggested key-word, that gives back interesting entries: john mullahy hurdle).

[Franci Taale]

Thanks for the advice, Carlo Lazzaro