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st: RE: what's an infinitesimal change in dprobit


From   "Maarten Buis" <M.Buis@fsw.vu.nl>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: RE: what's an infinitesimal change in dprobit
Date   Wed, 26 Oct 2005 19:25:59 +0200

It is d Pr(y=1)/dx1: the partial derivative of the predicted probability with respect to x1, while keeping all variables at specified values, usually the mean. It is interpreted as the change in probability for a unit change in x1 for a person with specified values on all variables, *if the effect would remain constant*.  The centred discrete change is an approximation of this, so it is not surprising that the two are often close. 

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu]On Behalf Of Tom Bonen
Sent: woensdag 26 oktober 2005 19:18
To: statalist@hsphsun2.harvard.edu
Subject: st: what's an infinitesimal change in dprobit

Hi Statalisters,

in the dprobit help it reads "dprobit reports the marginal effect,
that is the change in the probability for an infinitesimal change in
each independent, continuous variable and, by default, reports the
discrete change in the probability for dummy variables."

What does "infinitesmal change" mean here exactly?

I ran some models to investigate this and it turns out that the
dprobit coeffs are usually close but not always identical to the
centered discrete change coefficients (the change in Pr(Y=1) when
going from mean(x1)-1/2 to mean(x1)+1/2 (fixing the other covariates
at their means).

Or are the dprobit coeffs simply dF/dx w.r.t to x1 (i.e. the slope of
the partial derivative evaluated at the mean x1)? If yes, what would
be the exact interpretation this?

Thanks!

Best, Tom

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