Mike Will <[email protected]> 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
[email protected]
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