st: Proposal for a grid search for appropriate -nl- starting values

[Jonathan Beck <beck@wz-berlin.de>]

Dear Listeners,

although my experience with -nl- estimations is only a couple of months 
old, I noticed a frequent advice in Stata manuals, FAQs and Statalist 
regarding -nl- problems: "try different starting values".

Papers that present nonlinear least squares results often say they 
implement a "grid search" for starting values: they evaluate many 
different sets of starting values before chossing one for estimation. 
Accordingly, SAS allows you to specifiy a set of values for each 
parameter in your nonlinear function, calculates the sum of squared 
residuals (SSR) for each combination of starting values, and proceeds 
with estimation using that combination with the lowest SSR.

This approach seems reasonable to me, but I could not find a similar 
program for Stata. Did I miss something? Does it not make sense?

Anyhow, I tried to implement it myself, despite the fact that I am not 
an experienced Stata programmer. Below is the result.
It seems to work, but still there may be bugs and the code is most 
probably inefficient.

I would be happy to get your comments on this!

Two rather specific questions are listed below the code.

-----begin Stata code
version 8.2
  /* write your -nl- program (here: 3 parameters to be estimated)*/
program nlMyNLmodel
* (skipped)
end

  /* define grid of starting values: a vector for each parameter*/
matrix vA=(.05,.15,.25)
matrix vB=(.3,.6,.9)
matrix vC=(1,2,3)

  /* get SSR (sum of squared residuals) for all 3^3=27 combinations
    and remember those starting values that led to the lowest SSR */
local minssr=.
local bestlp = .
local bestls = .
local bestlth = .
forval i=1/3 {
  local sA`i'=vA[1,`i']
  forval j=1/3 {
    local sB`j'=vB[1,`j']
    forval k=1/3 {
      local sC`k'=vC[1,`k']
      capture nl MyNLmodel indepVariable, /*
                      */ init(A=`sA`i'',B=`sB`j'',C=`sC`k'') iterate(1) 
      if e(rss)<`minssr' {
        display "The lowest first-round SSR is currently " e(rss)
        local bestA = `sA`i''
        local bestB = `sB`j''
        local bestC = `sC`k''
        local minssr=e(rss)
        }
      }
    }
  }

  /* estimate nl-program for chosen set of starting values*/
display "Chosen starting values: A=`bestA', B=`bestB', C=`bestC'"
nl MyNLmodel indepVariable, init(A=`bestA',B=`bestB',C=`bestC')
-----end Stata code

1) The above procedure is not completely equivalent to one in SAS, 
because I obtain SSR values from -nl- results after, not before the 
first iteration (SSR at iteration 0 is not standard -nl- output, 
although it is displayed on the screen).
Methodologically, does it make a difference whether you evaluate the 
starting values before or after iteration 1?

2) Have other criteria than SSR been proposed for evaluating different 
starting values?

Thank you for reading this far!
Jonathan Beck
http://www.wz-berlin.de/mp/wiw/people/beck.en.htm
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