Re: The standard deviation of Three fitting parameters is bigger than

*To*: mathgroup at smc.vnet.net*Subject*: [mg100379] Re: The standard deviation of Three fitting parameters is bigger than*From*: "Sjoerd C. de Vries" <sjoerd.c.devries at gmail.com>*Date*: Tue, 2 Jun 2009 06:44:13 -0400 (EDT)*References*: <h00d2t$pkd$1@smc.vnet.net>

FindFit is not guaranteed to find a globally optimal fit, just locally. You can try various Methods for FindFit which are listed in tutorial/ UnconstrainedOptimizationIntroductionLocalMinimization In addition the Method->NMinimize can be used which is supposed to give you more globally optimal fits. Often, I construct a Manipulate function which with I fit the function interactively to my data (the sliders of the Manipulate are the parameters of the model). I use the values I obtain in that way as the starting values for the automatic fit. Cheers -- Sjoerd On Jun 1, 1:12 pm, holy... at gmail.com wrote: > I try to fit a formula, > 0.00138 t + 74.830*(t/a)^3*Integrate[(E^x x^4)/(E^x - 1)^2, {x, 0, a/ > t}] + n 3*8.314 (w/ t)^2 E^(w/ t)/(-1 + E^(w/t) )^2 > a,w,n are fitting parameters > t is indenpendt veriable > > First, I let a=375.362 to fit w and n. > FindFit[dataAl210K, {0.00138 t + 74.830*(t/375.362)^3*Integrate[(E^x > x^4)/(E^x - 1)^2, {x, 0, 375.362/t}] + n 3*8.314 (w/ t)^2 E^(w/ t)/(-1 > + E^(w/t) )^2}, {n, w},t] > I got {n -> 0.152124, w -> 1043.57} and the S.D.=0.150984 (standard > deviation) > > Then, I relax these there fitting parameters and give initial > conditions. > FindFit[dataAl210K, {0.00138 t + 74.830*(t/a)^3*NIntegrate[(E^x x^4)/ > (E^x - 1)^2, {x, 0, a/t}] > +n 3*8.314 (w/ t)^2 E^(w/ t)/(-1 + E^(w/t) )^2, {n > 0, a > 0, w > > 0}}, {{n, 0.15}, {a, 375}, {w, 1043}}, t] > Intuitively, the S.D. of three parameters should be smaller than two. > However, the S.D. of {n -> 0.904794, a -> 1921.19, w -> 259.28} is > 0.273892. > > I feel the answer is very close to the first one. > I think Mathematica may change the parameters too quickly,so the > caculation escape the local minimun of the first condition by only few > steps. > > Q:Can I constraint Mathematica to change the fitting parameters > slower? Don't escape the initial conditions I give too quickly. > (Can Nonlinearmodelfit do this?)