Re: st: nl command with restriction

["E. Paul Wileyto" <epw@mail.med.upenn.edu>]

Puzzled because your starting values don't add to 1 (a+b+c).  (If A+B+C 
add to 1, then you really are only estimating A & B.)  But if you do 
what I suggest, then the estimates you get back will not initially add 
to 1.  You must transform them back. 
If I read your function correctly:

	   	replace `1' = $a*((k^$b)*(l^$c)*(n^(1-$b-$c)))


replace $a in the expression with   exp($a)/(1+exp($a) +exp($b))

replace $b with   exp($b)/(1+exp($a) +exp($b))

replace $c with   1/(1+exp($a) +exp($b))

a, b, and c will come back with estimates from - to + infinity.

Then use nlcom to get back your parameter estimates:

nlcom (A: exp(_b[a])/(1+exp(_b[a]) +exp(_b[b]))) (B: 
exp(_b[b])/(1+exp(_b[a]) +exp(_b[b]))) (C: 1/(1+exp(_b[a]) +exp(_b[b])))

Paul





Rodolfo Coelho Prates wrote:

> Thanks Paul and Nick!
>
> I tried implement yours sugestions, but I think my comprehention is not
> correct.
>
> I estimeted the Cobb-Doulas with three variables, like this:
>
> program define nlces12
>          version 8.0
>          if "`1'" == "?" {
>              global S_1 "a b c"
> 	     global a=.15
>              global b=.4
>              global c=.3
>              global S_2 "Cobb-Douglas with additive error"
>                 exit
>             }
>
>
> 	   	replace `1' = $a*((k^$b)*(l^$c)*(n^(1-$b-$c)))
>
>
>        end
>
> This routine works well, but has that problem.
>
> If I understood, the suggestion is:
>
>
>
> 		replace `1' =
> $a*((k^(exp($b)/(1+exp($b)+exp($c))))*(l^(exp($c)/(1+exp($b)+exp($c))))*(n^(1/(1+exp($b)+exp($c)))))
>
>
>
>
>
> Thise are the estimations with brute force:
>
>   Source |       SS       df       MS            Number of obs =       123
> -------------+------------------------------         F(  2,   121) =   
> 102.83
>        Model |  8.2419e+09     2  4.1209e+09         Prob > F      =   
> 0.0000
>     Residual |  4.8489e+09   121  40073949.1         R-squared     =   
> 0.6296
> -------------+------------------------------         Adj R-squared =   
> 0.6235
>        Total |  1.3091e+10   123   106429266         Root MSE      = 
> 6330.399
>                                                      Res. dev.     =  
> 2500.31
> Cobb Douglas with aditive error
> ---------------------------------------------------------------------------
>            y |   Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
> -------------+-------------------------------------------------------------
>            a | 2.594492  .3699407     7.01   0.000     1.862096    3.326887
>            b | 17.12698  .3519304    48.67   0.000     16.43025    17.82372
>            c | 16.97066      .        .       .            .           .
> ------------------------------------------------------------------------------
>
> Works well, but the sum of coeficients are larger than one, but not
> negatives. Do I need realize a transformation? Or did I made something
> wrong?
>
> Best Regards,
>
> Rodolfo
>
>
> *
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>
>   
--
E. Paul Wileyto, Ph.D.
Assistant Professor of Biostatistics
Tobacco Use Research Center
School of Medicine, U. of Pennsylvania
3535 Market Street, Suite 4100
Philadelphia, PA  19104-3309

215-746-7147
Fax: 215-746-7140
epw@mail.med.upenn.edu
http://mail.med.upenn.edu/~epw/ 
*
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