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Re: st: mfx algorithsm for standard error


From   rgutierrez@stata.com (Roberto G. Gutierrez, StataCorp.)
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: mfx algorithsm for standard error
Date   Tue, 03 Sep 2002 17:43:11 -0500

Mike Will <mystata@hotmail.com> has asked about the formula for the standard
errors calculated by -mfx-, and now writes:

> I have checked into mfx using findit mfx and couldn't get much out of it.
> Most of the explanations are too short and didn't even touch upon the
> standard errors of marginal effects.  Any more inputs from those who wrote
> it or some other good references talking about the standard errors
> especially for the nonlinear options?  Appreciate it.

The standard errors of the marginal effects are calculated using the "delta
method", which basically says that if you have a continuous function of some
estimators (like a marginal effect), then the standard error of this function
can be obtained from the derivatives of this function with respect to the 
estimators in question and the variance-covariance matrix of the original 
estimators.  

See

http://www.stata.com/support/faqs/stat/deltam.html

for Al Feiveson's excellent explanation of the delta method.  In -mfx- the
derivatives are calculated numerically.  Most of the time, the marginal effect
is such that it is a function of the whole linear predictor, x*beta, rather
than a function of each individual beta.  When this occurs, this simplifies
the standard error calculation significantly since you can treat x*beta as a
scalar random quantity, rather than having to consider the marginal effect as
a function of each individual component of beta -- fewer derivatives to take.

--Bobby
rgutierrez@stata.com
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