Dean Yang <[email protected]> asks:
>> Is there a non-linear analog to the -lincom- command? I'd like to calculate
>> a nonlinear function of some regression coefficients, and the associated
>> standard error.
>> I know we can test nonlinear hypotheses using -testnl-, but the command only
>> saves chi or F-statistics and degrees of freedom. It doesn't give you the
>> standard error on the estimate.
and John Gibson <[email protected]> replied:
> From testnl, if you use the
> ... ,g(matname)
> option you can save the Jacobian, and then plug that into the delta method
> formula.
To elaborate on what John suggests, I'll give an example using the auto data.
We begin by fitting a linear regression
. regress price weight length mpg
[some output omitted]
------------------------------------------------------------------------------
price | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
weight | 4.364798 1.167455 3.74 0.000 2.036383 6.693213
length | -104.8682 39.72154 -2.64 0.010 -184.0903 -25.64607
mpg | -86.78928 83.94335 -1.03 0.305 -254.209 80.63046
_cons | 14542.43 5890.632 2.47 0.016 2793.94 26290.93
------------------------------------------------------------------------------
Suppose then that our nonlinear combinations of parameters is
f(b) = _b[length]/_b[mpg]
that is, the ratio of the coefficients on -length- and on -mpg-.
We call -testnl- with a test of f(b) = 0, and retrieve the matrix of first
derivatives (the Jacobian), G.
. testnl _b[length]/_b[mpg] = 0, g(G)
(1) _b[length]/_b[mpg] = 0
F(1, 70) = 1.05
Prob > F = 0.3099
. mat list G
G[1,4]
c1 c2 c3 c4
r1 0 -.01152216 .01392232 0
We note that the derivatives of f(b) with respect to the first and last
element of e(b), namely _b[weight] and _b[_cons], are zero. That's comforting
considering that f(b) is not a function of these two parameters.
Applying the delta method,
. mat A = G*e(V)*G'
. mat list A
symmetric A[1,1]
r1
r1 1.3953568
gives the estimated variance.
--Bobby
[email protected]
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