Re: st: nl-command sensitive (sometimes) to unit of measurement

["Brian P. Poi" <bpoi@stata.com>]

On Tue, 9 Sep 2008, Lina Jonsson wrote:

> Dear all,
>
> I have encountered a strange phenomenon using the nl-command. I am 
> estimating a model on two subsets. Among the independet variables are 
> two variables that measure a distance and when I changed the unit from 
> meters into km the estimates of other variables in the models changed 
> (by a substantial amount) for one of the subsets but not the other.
...
> b1 is 0.56 when the distance variables are measured in meters and 0.48 
> when measured in km, a quite large difference. Any suggestions how to 
> deal with this?
A couple of thoughts come to mind.  First, you might try specifying 
eps(1e-8) or eps(1e-9) before you fit the model.  That controls the 
convergence criterion.  You might find that by tightening that up, the 
model does in fact converge to the same solution whether you use meters or 
kilometers.

Second, in linear regression if you multiply a regressor by 1000 then you 
will get the same parameters, except the parameter for the regressor you 
multiplied by 1000 will be 1/1000th of its original value.  However, that 
property is not always true for nonlinear models.  Here is a trivial 
example to illustrate that point:

   . sysuse auto
   . nl (mpg = {b0} + {b1}*exp(1/gear))

         mpg |      Coef.   Std. Err.      t    P>|t|
   --------------------------------------------------
         /b0 |   88.36907    10.4828     8.43   0.000
         /b1 |  -47.71047   7.446863    -6.41   0.000

   . replace gear = gear / 10
   . nl (mpg = {b0} + {b1}*exp(1/gear))

         mpg |      Coef.   Std. Err.      t    P>|t|
   ----------+---------------------------------------
         /b0 |   27.02461    1.16402    23.22   0.000
         /b1 |  -.1680976   .0298792    -5.63   0.000


Thus, the fact that there are 1000 meters in 1 kilometer does not 
automatically imply that whether you use meters or kilometers will just 
affect your b1 parameter by a factor of 1000.

Third, you might try using slightly different starting values.  Do the 
starting values you use affect the final results?

   -- Brian Poi
   -- bpoi@stata.com

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