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From |
"Austin Nichols" <austinnichols@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

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

Date |
Thu, 20 Dec 2007 08:44:35 -0500 |

Henrique Neder <hdneder@ufu.br>: The FAQ by Feiveson addresses finding solutions to an equation of the form f(x)=0 where f() is a vector-valued function of a vector x, not estimating a nonlinear SUR model, which is done via the command -nlsur- in Stata10: http://stata.com/help.cgi?nlsur As for the first problem--finding zeros of some function f(x)--there is now a better solution in Stata 10. Use -optimize- in Mata to minimize the sum of elements of f(x) using evaluator type v0, or minimize crit=f(x)'f(x) using evaluator type d0. Or calculate the gradient of f(x) and use d1 or v1, or the Hessian to use d2 or v2. See http://stata.com/help.cgi?mf_optimize for more details. Or consider this example: Suppose you wanted to find the zeros in y = x^2 – 5*x + 4 and you were too lazy to use the quadratic formula. I chose this problem, of course, because it has multiple solutions (illustrating the importance of starting values) and its analytic solution is so easy, whereas the numerical methods are trickier. You could just type void q(todo,b,crit,g,H) { crit=(b^2-5*b+4)^2 } sol=J(1,0,0) void grid(n1,n2) { external sol, p for (i=n1; i<=n2; i++) { init=i S=optimize_init() optimize_init_evaluator(S, &q()) optimize_init_which(S,"min") optimize_init_evaluatortype(S,"d0") optimize_init_params(S,init) p=round(optimize(S),10e-4) if (!anyof(sol, p)) { sol=(sol,p) } } sol } grid(-10,10) The above code does the optimization for every starting value on a grid over the integers -10 to 10 (and saves any solutions that are new to a Mata variable sol, then reports its values). A function that took a vector as an argument would be no harder to specify (though the appropriate grid search might be harder to specify). On Dec 20, 2007 7:32 AM, Henrique Neder <hdneder@ufu.br> wrote: > 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 * * 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: Estimation of a non-linear system of equations***From:*Craig Martin <craigmar@uoguelph.ca>

**st: RES: Estimation of a non-linear system of equations***From:*"Henrique Neder" <hdneder@ufu.br>

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