# st: THANKS SO MUCH! RE: Derivatives at different parameter values

 From "J Page" To statalist@hsphsun2.harvard.edu Subject st: THANKS SO MUCH! RE: Derivatives at different parameter values Date Wed, 24 Mar 2004 12:47:04 -0500

```Dear Alan,

Thanks very much.  I will give it a try.

John

```
From: "FEIVESON, ALAN H. (AL) (JSC-SK) (NASA)" <alan.h.feiveson@nasa.gov>
To: "'statalist@hsphsun2.harvard.edu'" <statalist@hsphsun2.harvard.edu>
Subject: st: RE: Derivatives at different parameter values
Date: Wed, 24 Mar 2004 09:00:49 -0600

John - Let's see if I understand your question. You have some function
f(th_1, th_2,...th_n) and you want Stata to calculate df/dth_k at particular
values of th_1, th_2,..,th_n.

If this is what you want, there is a way you can do it by setting up a fake
regression and using _testnl. Here's an example:

Suppose your function is (th_2)/(th_3) - exp(-th_1), and you want to
evaluate the partial derivatives of f at (th_1, th_2, th_3) = (2,3,6).

Set up a fake dataset and regression as follows:

.clear
.set obs 3
.gen temp=_n
.tab temp,gen(dum)
.gen y=2*dum1+3*dum2+6*dum3
.reg y dum1 dum2 dum3,noc

Then use -testnl- with the "g" option to save the matrix of partial
derivatives:

.testnl _b[dum2]/_b[dum3]-exp(-_b[dum1])=1,g(G)

The result of the test will be undefined (since the regression is a perfect
fit), but the matrix G will contain the partial derivatives you want.

In this example, df/dth_1 = exp(-th_1), df/dth_2 = 1/th_3 and df/dth_3 =
-th_2/(th_3)^2.
So the G matrix should contain exp(-2), 1/6 and -3/36.

If you want to implement this for ranges of parameter values, you would have
to incorporate this as part of a do-file.

Al Feiveson

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu]On Behalf Of J Page
Sent: Tuesday, March 23, 2004 2:17 PM
To: statalist@hsphsun2.harvard.edu
Subject: st: Derivatives at different parameter values

Hi,

How can one implement the numerical derivatives currently implemented in
Stata's ml maximizer in a setting outside outside of ml? I would like to
calculate numerical derivatives at given parameter values. The dydx function

does not appear to do this.

Thanks much.

John

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