CODEWITHSUNDEEP
wolfram-mathematica
Luis Martinez
Luis Martinez

Reputation: 13

Why is my nonlinear model fitting in mathematica not providing small figures?

#dataset, sigmoidal curve
ratio278a267 ={{5.445, 0.0501}, {6.177, 0.035}, {7., 0.0589}, {7.368, 
  0.0953}, {7.73, 0.1419}, {8.169, 1.0697}, {9.141, 1.0869}, {10.3, 
  1.0981}} 

#nonlinearmodelfitting for dataset
fit = FindFit[ratio278a267, (1/(a + (E^(-b*(x - c))))), {a, b, c}, x]
fit2 = NonlinearModelFit[
   ratio278a267, (1/(a + (E^(-b*(x - c))))), {a, b, c}, x]["RSquared"]

#fit1 & fit2 output respectively
output:
{a -> 0.639719, b -> -250.201, c -> -1008.92}
0.

The code above is what i used for a nonlinear fitting in Mathematica, and the output has not provided reasonably small figures, despite me having plotted this in a graphing calculator overlaid ontop of my dataset, with numbers between 0-10 for a,b,c and have obtained reasonable fitting

Upvotes: 1

Views: 559

Answers (1)

Bill
Bill

Reputation: 3977

One way to get FindFit to converge on a good solution is to give it good starting values, particularly when your model could give wildly bad fits for some values of the values.

x=.;a=.;b=.;c=.;
ratio278a267 ={{5.445, 0.0501}, {6.177, 0.035}, {7., 0.0589}, {7.368,0.0953},
  {7.73, 0.1419}, {8.169, 1.0697}, {9.141, 1.0869}, {10.3,1.0981}};
fit = FindFit[ratio278a267, (1/(a+(E^(-b*(x-c))))), {{a,0.92}, {b,8.7}, {c,7.9}}, x]
Show[ListPlot[ratio278a267],Plot[(1/(a+(E^(-b*(x-c)))))/.fit,{x,5.445,10.3}]]

In this example I found those starting values by doing ten thousand Monte Carlo trials looking for the smallest sum of squared error between the model and the data points and then let FindFit converge on the best values that it could find.

Upvotes: 1

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