Difference between nlcom and margins

[Chiara Piazzo]

Dear all,

I am running the following regression;

svy linearized: tpoisson hours i.year_season i.location c.temp#i.location c.age##c.age* i.gender i.race i.health* c.income##c.income exp c.tar##c.tar

My goal is to compute the turning point for the variable tar and I do so using;

nlcom -_b[tar]/(2*_b[c.tar#c.tar])

However, I also compute the marginal effects using;

margins, at(tar = (12(1)43)) vsquish

The output from margins shows that the point where hours is maximized is much lower (24 compared to 27 from nlcom). I am trying to understand where this difference comes from?

Is there a way to reconcile the results from nlcom and margins? Any help will be greatly appreciated. Thank you!

Sincerely,

Milu

[Phil Bromiley]

You didn't get a quick answer. I don't work with tpoisson or svy, but when I tried to replicate your problem, it did not work. Please start a new post including sample data using dataex so we can replicate your problem.

[Dimitriy V. Masterov]

Setting the -svy- part aside, you are neglecting that in Poisson models, you actually have E[y | x] = exp(a +b*x + c*x^2), so you are optimizing the wrong function by ignoring exp{} in your first calculation. Here's an example showing that the two ways agree:

webuse runshoes, clear
tpoisson shoes c.age##c.age, coefl
nlcom margins_at_age_16:exp(_b[_cons] +  _b[c.age]*16 + _b[c.age#c.age]*16^2)
margins, at(age = (16(1)54))
marginsplot, addplot(function exp(1.323112 -.0492211*x +  .0009251*x^2), range(16 54) lpatter(dash) lcolor(red)) xline(26.603) noci

[Chiara Piazzo]

Dear Dimitriy V. Masterov, thank you very much for your reply and the solution. Your code is very useful!

I had a question about the following part;

nlcom margins_at_age_16:exp(_b[_cons] +  _b[c.age]*16 + _b[c.age#c.age]*16^2)

why multiplying by 16 though? Thanks again!

Sincerely,

Chiara

[Dimitriy V. Masterov]

I am calculating predicted shoes at age 16, so it matches the first margins.

[Chiara Piazzo]

Dear Dimitriy V. Masterov, thank you so much! Appreciate it.

Sincerely,

Chiara