# Re: st: Estimating marginal effects of linear and quadratic term from a logit regression

 From "maartenbuis" To statalist@hsphsun2.harvard.edu Subject Re: st: Estimating marginal effects of linear and quadratic term from a logit regression Date Mon, 08 Nov 2004 09:15:57 -0000

```Dear Pradeep,

Calculating the marginal effect for a logistic regression when one of
the explanatory variables is also entered with an quadratic term can
be done by `hand' (well, by -nlcom- actually) but it gets a bit ugly,
see the example below.

Notice that the first couple of lines of the -nlcom- is the
probability density function of the logistic: exp(xb)/(1+exp(xb))^2.
The last lines of the -nlcom- command is the derivative of xb with
respect to x of interest, in this cas mpg: _b[mpg]+2*_b[mpg2]*(mean
mpg).

Maarten

#delim ;
sysuse auto;

gen mpg2=mpg^2;

logit foreign price weight mpg mpg2;

sum price, meanonly;
local price = r(mean);

sum weight, meanonly;
local weight = r(mean);

sum mpg, meanonly;
local mpg = r(mean);

nlcom(
exp(_b[_cons] + _b[price]*`price' + _b[weight]*`weight' + _b
[mpg]*`mpg' + _b[mpg2]*`mpg'^2)/
(1+exp(_b[_cons] + _b[price]*`price' + _b[weight]*`weight' + _b
[mpg]*`mpg' + _b[mpg2]*`mpg'^2))^2*
(_b[mpg]+2*_b[mpg2]*`mpg')
);

> I have a logit model with a linear and quadratic variable along
with some
> other variables (call it stuff). I am trying to estimate the
marginal
> effects for different sets variables in my model where each set is
comprised
> of a linear and quadratic term. Is there a ado file for this that
does not
> require the differentiation to be done manually (and then run a
proceedure
> like nlcom) or is that the best there is?

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```