st: Re: xtnbreg - same results after convergence at 9,000 iterations or limiting to 100 iterations

[Gordon Hughes <G.A.Hughes@ed.ac.uk>]

A somewhat belated response since no-one has picked this up.

I am not familiar with the programming details of -xtnbreg- but the 
strategy is obvious.  It is common to generate good starting values 
for difficult ML procedures by estimating a restricted version of the 
model, whose parameters can be used a starting values for maximising 
the more general likelihood function.  This is what -xtnbreg- is 
doing.  The problem for you is that the restricted model, usually 
assumed to be easy to maximise, is in fact degenerate or very nearly 
degenerate.  Hence the initial maximisation stage is taking a very 
long time to find a maximum, which may not even exist.  However, once 
you feed any plausible set of starting values to the full 
maximisation, the procedure converges rapidly.  The -xtnbreg- 
procedure appears to be unusual because it goes through the process 
of generating starting values in two steps.  The degeneracy that is 
causing problems is in the first step and disappears at the second 
step, which produces good starting values for the final stage of full 
maximisation.

The lesson to draw is that it is rarely, if ever, worth allowing the 
first stage of a multi-stage maximisation to run for a lot of 
iterations, unless you happen to be interested in the results of the 
first stage.  You should consider the possibility that your model is 
not well-defined because failure or close to failure in estimating a 
simple version of the model may be a warning that the results from a 
more complex version are merely the by-product of assumptions that 
you have imposed rather than the information in your sample.

Gordon Hughes
g.a.hughes@ed.ac.uk
 

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