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Re: st: -nlcom-, delta method, and the derivative

From   [email protected] (Roberto G. Gutierrez, StataCorp)
To   [email protected]
Subject   Re: st: -nlcom-, delta method, and the derivative
Date   Sun, 23 Jan 2011 10:55:32 -0600

Kristian Karlson <[email protected]> writes:

> I am using -nlcom- to get the standard error of a complex transformation of
> a regression coefficient of interest. -nlcom- applies the delta method to
> get the standard error. I have also done manual calculations of the standard
> error. However, I obtain different results than those produced by -nlcom-. A
> Monte Carlo study moreover suggests that the SE produced by -nlcom- is much
> better than my manual calculation. I would like to inspect the differences,
> because I suspect the differences to exist in the derivatives.

> Is it possible for me to obtain the derivative calculated by -nlcom-? I
> haven't been able to find any information on this. In the documentation, I
> would like to see the G in GVG'.

Not directly from -nlcom-, but you can get the equivalent from -testnl-, which
is called by -nlcom- anyway.

    . sysuse auto, clear
    . regress mpg foreign
    . nlcom (_b[foreign])^2
    . testnl (_b[foreign])^2 = 0

-testnl- returns the derivative matrix in r(G):

    . return list
    . mat list r(G)

the second element of which (the derivative of the expression wrt -foreign-, 
the second coefficient of e(b)) will coincide with 

    . di 2*_b[foreign]

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