RE: Rép. : st: RE: Initial values in -nl-

["Brian P. Poi" <brian@poiholdings.com>]

On Sunday, November 14, 2010 3:11 AM Herve STOLOWY wrote:

Thank you very much. It now works. I only have another problem with my coefficients but I will create a new thread.

Apart from that, would you know where I could get some explanation on the meaning of initial values? (For the moment, all my initial values are equal to one but I do not understand what it represents).

----

In order for any nonlinear optimizer to work, it needs a set of initial values at which it can calculate the objective function.  Then the optimizer can analyze the function at that point (namely, look at the derivatives) and hopefully find a new set of parameters that results in a higher or lower value for the objective function (depending in whether it is maximizing or minimizing the function).  It can then repeat that procedure to keep finding better parameters.

But for the optimizer to get started, it needs an initial set of values at which the function can be computed.  By default, -nl- sets all the parameters to zero.  -ml- does the same thing, but -ml- has additional algorithms implemented that try and improve on the initial values before using the (quasi-)Newton optimizer.

Maximum Likelihood Estimation With Stata (4th ed.) (fair disclosure, I'm a coauthor) has a section in chapter 1 that discusses optimization along with references to texts that discuss optimization in more detail.  The algorithm that -nl- uses is discussed in Davidson and MacKinnon's 1993 text Estimation and Inference in Econometrics.

   -- Brian Poi
   -- brian@poiholdings.com



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