st: Formula for standard error of predicted probability in logit model

[Lucas <lucaselastic@gmail.com>]

Dear statalisters,

I have found many references to the multiple ways one can calculate a
predicted probability from a logit model in stata (and in programs
varying from excel to R).  What I have been unable to find is the
formula stata uses to calculate the standard error of the predicted
value estimate.   I've looked through the stata manuals and could not
find the formula.  I checked Long & Freese and they convey the
commands but not the formulas (at least as far as I could see).  I
could just treat the predicted value as a linear combination and use
the rules for the variance of a linear combination, but I am not sure
that'd be correct (as it is a nonlinear function).  Some works
reference the delta method, but I am not sure that's what stata uses.

So, my question--can someone convey formulas for the variance (or
standard error) of the calculated predicted value(s) from a logit
model, or direct me to a source that contains the formula(s)?

I appreciate your help!

Sam
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