st: Using for within Mata optimize to loop over observations

[Bob Hammond <robert_hammond@ncsu.edu>]

All,

Using Mata's optimize(), I want to find the x that maximizes f(x,z) with 
respect to x, where z is a variable in my existing data set.  My thought 
is to loop over observations, feeding in the z of the current 
observation and storing the optimum in the current observation's x.  My 
problem is that I cannot get a for loop to work within the optimize code. 

Another solution is to differentiate f(x,z) with respect to x and find 
the x that makes the derivative equal to zero for each z in the data 
set.  This works perfectly for several versions of f(x,z) but I am now 
working with an f(x,z) that is much more easily expressed without having 
to differentiate.  Also, since I am currently trying to learn Mata, I 
would like to know how to use loops within the optimize code since it 
seems like a reasonable thing to do.

The most closely related solution I found in a search of the archives is 
http://www.stata.com/statalist/archive/2007-12/msg00551.html but I 
haven't been able to translate this solution to my problem of loop over 
observations.

The following code uses a trivial f(x,z) and shows how to do it with 
mm_root() (which works) and one way that seems like it might work with 
optimize() (which does not).  I've tried several versions of the 
optimize() approach (basically moving around the "for(...)") but it 
always either gives an error, uses only the first observation, or uses 
only the last observation.

Ben Jann's moremata package is required to use mm_root() (-findit 
moremata-).

Thanks in advance for any thoughts,

Bob

>>>>>>>>>>>
clear
clear mata
set obs 10
gen double z  = runiform()
gen double x  = .
gen double x2 = .
mata:
   function myfunc(x,z) return(-2*(x-z))
   for(i=1;i<=st_nobs();i++) {
       z = st_data(i,"z")
       rc = mm_root(x = ., &myfunc(), 0, 1, 0, 1000, z)
       st_store(i,"x",x)
   }
   void eval0(todo, x, v, g, H)
   {   
       z = st_data(i,"z")
       v = -(x-z)^2
   }
   for(i=1;i<=st_nobs();i++) {
       S = optimize_init()
       optimize_init_evaluator(S, &eval0())
       optimize_init_params(S, 0)
       x = optimize(S)
       st_store(i,"x2",x)
   }
end
list

--
------------------------------------------------------------------------
Bob Hammond
Department of Economics
North Carolina State University
Office: (919) 513-2871
Fax: (919) 515-7873
http://www4.ncsu.edu/~rghammon/

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