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From |
"Henrique Neder" <hdneder@ufu.br> |

To |
<statalist@hsphsun2.harvard.edu> |

Subject |
st: RES: Estimation of a non-linear system of equations |

Date |
Thu, 20 Dec 2007 10:32:54 -0200 |

I copied the following answer to FAC due to Feiveson. I hope that this help you. Henrique How can I use Stata to solve a system of nonlinear equations? Title Using Stata to solve a system of nonlinear equations Author Alan H. Feiveson, NASA Date June 2001; updated October 2005 ---------------------------------------------------------------------------- ---- Suppose that you want to solve f1(a1,...,an) = 0 f2(a1,...,an) = 0 . . . fn(a1,...,an) = 0 (n nonlinear equations in n unknowns a1,..,an) First, rewrite the first equation such that its right-hand side is 1: f1(a1,...,an) + 1 = 1 f2(a1,...,an) = 0 . . . fn(a1,...,an) = 0 Then, set up a fake dataset with n observations as follows: The dependent variable y takes on the value 1 for the first observation and 0 for all the others. Stata's nl estimation won't work if y is a constant, so you need to write the first equation so that the "right-hand sides" are not all the same; that is why I reformulated the problem above. In this example, I used one for the first observation and zero for the others. Write an nl program that fills in the dependent variable passed to it with the values of the functions. Suppose n=3. Then your program should look something like this: program nlfaq syntax varlist (min=1 max=1) [if], at(name) tempname a1 a2 a3 scalar `a1' = `at'[1, 1] scalar `a2' = `at'[1, 2] scalar `a3' = `at'[1, 3] tempvar yh generate double `yh' = f1(`a1', `a2', `a3') in 1 replace `yh' = f2(`a1', `a2', `a3') in 2 replace `yh' = f3(`a1', `a2', `a3') in 3 replace `varlist' = `yh' end nl requires that our program accept an if clause, though we can ignore it in our program since we do not have missing data and will not be restricting the estimation sample when calling nl. Call nl with y as the dependent variable, specifying initial values for a1, a2, ..., an at which the functions can be evaluated. Here is an example. Suppose that I want to solve the following system for A, B, and C: exp(A) + B*C = 3 A/B + C^2 = log(B) A/(A+B+C) = sin(C) Here is my nl program: program nlfaq syntax varlist(min=1 max=1) [if], at(name) tempname A B C scalar `A' = `at'[1, 1] scalar `B' = `at'[1, 2] scalar `C' = `at'[1, 3] tempvar yh gen double `yh' = exp(`A') + `B'*`C' - 2 in 1 replace `yh' = `A'/`B' + `C'^2 - log(`B') in 2 replace `yh' = `A'/(`A'+`B'+`C') - sin(`C') in 3 replace `varlist' = `yh' end Now I generate the dataset that nl requires: . clear . set obs 3 obs was 0, now 3 . generate y = 0 . replace y = 1 in 1 (1 real change made) I estimate using nl: . nl faq @ y, parameters(A B C) initial(A 1 B 1 C 1) (obs = 3) Iteration 0: residual SS = .5792985 Iteration 1: residual SS = .0364809 Iteration 2: residual SS = .0001378 Iteration 3: residual SS = 2.92e-09 Iteration 4: residual SS = 1.43e-18 Iteration 5: residual SS = 2.25e-31 Source | SS df MS -------------+------------------------------ Number of obs = 3 Model | 1 3 .333333333 R-squared = 1.0000 Residual | 1.6332e-31 0 . Adj R-squared = . -------------+------------------------------ Root MSE = . Total | 1 3 .333333333 Res. dev. = -207.451 ---------------------------------------------------------------------------- -- y | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+-------------------------------------------------------------- -- /A | .8973072 . . . . . -------------+-------------------------------------------------------------- -- /B | 1.803287 . . . . . -------------+-------------------------------------------------------------- -- /C | .3033412 . . . . . ---------------------------------------------------------------------------- -- * (SEs, P values, CIs, and correlations are asymptotic approximations) Finally, I verify the solution: . scalar A = [A]_b[_cons] . scalar B = [B]_b[_cons] . scalar C = [C]_b[_cons] . di exp(A) + B*C 3 . di A/B + C^2 " " log(B) .58961117 .58961117 . di A/(A+B+C) " " sin(C) .29871053 .29871053 -----Mensagem original----- De: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] Em nome de Craig Martin Enviada em: quarta-feira, 19 de dezembro de 2007 17:14 Para: statalist@hsphsun2.harvard.edu Assunto: st: Estimation of a non-linear system of equations I am using Stata 9 and need to estimate a system of equations. I can estimate each equations separately using nl. However, when I try to estimate the system using the same syntax as linear estimation for a system of equations, I get a varlist error. What is the syntax or how do you estimate a non-linear system of eqation in Stata 9.0? Thanks, -- Craig Martin M.Sc. PhD Candidate Department of Food, Agricultural and Resource Economics University of Guelph Guelph, Ontario N1G 2W1 (519) 824-4120 Ext. 58315 Fax (519) 767-1510 * * 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/ No virus found in this incoming message. Checked by AVG Free Edition. Version: 7.5.503 / Virus Database: 269.17.4/1187 - Release Date: 16/12/2007 11:36 No virus found in this outgoing message. Checked by AVG Free Edition. Version: 7.5.503 / Virus Database: 269.17.4/1187 - Release Date: 16/12/2007 11:36 * * 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/

**Follow-Ups**:**Re: st: RES: Estimation of a non-linear system of equations***From:*"Austin Nichols" <austinnichols@gmail.com>

**References**:**st: Estimation of a non-linear system of equations***From:*Craig Martin <craigmar@uoguelph.ca>

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