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From |
"E. Paul Wileyto" <[email protected]> |

To |
[email protected] |

Subject |
Re: st: nl command with restriction |

Date |
Tue, 12 Feb 2008 08:09:08 -0500 |

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

[email protected]

http://mail.med.upenn.edu/~epw/

*

* For searches and help try:

* http://www.stata.com/support/faqs/res/findit.html

* http://www.stata.com/support/statalist/faq

* http://www.ats.ucla.edu/stat/stata/

**References**:**st: truncreg with panel data***From:*Anita <[email protected]>

**st: RE: truncreg with panel data***From:*Even Bergseng <[email protected]>

**st: nl command with restriction***From:*"Rodolfo Coelho Prates" <[email protected]>

**Re: st: nl command with restriction***From:*"E. Paul Wileyto" <[email protected]>

**RE: st: nl command with restriction***From:*"Nick Cox" <[email protected]>

**Re: st: nl command with restriction***From:*"E. Paul Wileyto" <[email protected]>

**RE: st: nl command with restriction***From:*"Nick Cox" <[email protected]>

**Re: st: nl command with restriction***From:*"E. Paul Wileyto" <[email protected]>

**Re: st: nl command with restriction***From:*"Rodolfo Coelho Prates" <[email protected]>

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