Re: st: -margins- and ratio interactions

[Richard Williams <richardwilliams.ndu@gmail.com>]

One of my ongoing wish list items for Stata is that factor variables 
be expanded to include more variable functions, e.g. log of x, 1/x, ratios.

For now, the main thing I can think of is to specify specific values 
you want plotted/computed. So, it might be something like mpg = 30, 
m_mpg = 1/30, weight = 2000, weight_mpg = 2000/30, or whatever, i.e. 
you know what the ratio term should equal so go ahead and compute it 
and plug it in, and do this for several relevant values. This might 
be quite tedious of course, and not having tried it I am not sure it 
will work right.

At 09:56 AM 3/11/2014, Federico Belotti wrote:
> Dear listers,
>
> I'm trying to use -margins- to get marginal effects (at means) when 
> the model includes an interaction between two variables that is a ratio.
>
> In the standard case (when the interaction between two variables is 
> a product), there are no issues thanks to the Stata -factor variables- syntax
>
> ===== code begins ====
> sysuse auto, clear
> **** Product
> reg price mpg weight c.mpg#c.weight
> sum mpg, mean
> local m_mpg = r(mean)
> sum weight, mean
> local m_weight = r(mean)
> lincom _b[weight] + _b[c.mpg#c.weight]*`m_mpg'
> lincom _b[mpg] + _b[c.mpg#c.weight]*`m_weight'
> margins, dydx(weight) at((mean) mpg)
> margins, dydx(mpg) at((mean) weight)
> ===== code ends ====
>
> On the other hand, I'm using the following code to get marginal 
> effects (at means) when the model includes a ratio interaction
>
> ===== code begins ====
> sysuse auto, clear
> **** Ratio
> gen mpg_1 = 1/mpg
> reg price mpg weight c.mpg_1#c.weight
> sum mpg, mean
> local m_mpg = r(mean)
> sum weight, mean
> local m_weight = r(mean)
> nlcom _b[weight] + _b[c.mpg_1#c.weight]*(1/`m_mpg')
> nlcom _b[mpg] + _b[c.mpg_1#c.weight]*(-`m_weight'/`m_mpg'^2)
> margins, dydx(weight) at(mpg_1 = `=1/`m_mpg'')
> margins, dydx(mpg) at(weight = `m_weight' mpg_1 = `=-1/`m_mpg'^2')
> ===== code ends ====
>
> While it is easy to recover the correct marginal effect for the 
> variable at the numerator of the ratio (in this case "weight"), I'm 
> struggling to get the correct marginal effect for the denominator 
> variable (in this case "mpg"). The problem here is that Stata does 
> not recognize "mpg_1" as the inverse of "mpg" and -margins- forgets 
> the interaction term in the computation.
>
> Am I doing something wrong? Is there a smart way to write the 
> -margins- syntax in order to recover mpg's marginal effect?
>
> Any hint is really appreciated.
> Thanks.
>
> Ciao,
> Federico
>
> --
> Federico Belotti, PhD
> Research Fellow
> Centre for Economics and International Studies
> University of Rome Tor Vergata
> tel/fax: +39 06 7259 5627
> e-mail: federico.belotti@uniroma2.it
> web: http://www.econometrics.it
>
>
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-------------------------------------------
Richard Williams, Notre Dame Dept of Sociology
OFFICE: (574)631-6668, (574)631-6463
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