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Re: st: could not calculate numerical derivatives -- flat or discontinuous region encountered


From   "JVerkuilen (Gmail)" <jvverkuilen@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: could not calculate numerical derivatives -- flat or discontinuous region encountered
Date   Sun, 30 Dec 2012 11:19:39 -0500

On Sun, Dec 30, 2012 at 8:39 AM, Usman Gilani <ujgilani@gmail.com> wrote:
> Dear member,
> Thanks for your quick reply. I'm trying to run models as you suggested. I'm new to stata and econometrics, could you please elaborate what do you mean by  "...empirical identification or else some other specification error".>

A model that's empirically unidentified is one that is formally
identified, that is it's possible with *some* dataset to get valid
estimates, but for *your* dataset it's not.

Here's a simple example: Linear regression with a binary predictor. If
the binary predictor is mostly 0s with only a few 1s because the
binary variable is tracking a rare event. In a small sample, it's
reasonably likely for there to be no observed events, and thus the x
variable would drop out of the regression model due to there being no
variance. The regression model itself is identified, but will be
empirically unidentified whenever no events occur on x. In the
ordinary linear model you don't hear these terms but they still apply
and would be called something else, such as collinearity.

By valid estimates, I mean that the Hessian is positive definite, the
estimates are at an interior point on the parameter space,
etc.Somewhere there's the equivalent of a divide by 0 created by a
variable that's effectively become a constant, perfect separation on a
logistic regression, or the like.

With a complex model such as the one you specified it can be quite
difficult to track this problem down, which is why my advice is to
roll back to a simpler model and then deliberately build up to the
complicated model.

But of course I am not an expert at what you're trying to run, in
particularly not a substantive expert, so you need to decide that for
yourself and hopefully get advice from someone who is.
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