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I'm trying to use NonlinearModelFit to fit the data:

Data = {{2.046204620462046`, 1.274347668`}, {2.012987012987013`, 
    1.131369542`}, {1.984`, 0.939944276`}, {1.952755905511811`, 
    0.721156437`}, {1.9224806201550388`, 
    0.614591638`}, {1.8931297709923665`, 
    0.572324748`}, {1.8674698795180722`, 
    0.536605273`}, {1.8397626112759644`, 
    0.49948005`}, {1.8128654970760234`, 
    0.478452409`}, {1.7867435158501441`, 
    0.455583518`}, {1.7613636363636365`, 
    0.439702881`}, {1.7342657342657342`, 
    0.411870668`}, {1.712707182320442`, 
    0.365204419`}, {1.6870748299319729`, 
    0.303633546`}, {1.6666666666666667`, 
    0.232056102`}, {1.6445623342175066`, 
    0.140710942`}, {1.6230366492146597`, 
    0.070744185`}, {1.6020671834625324`, 
    0.035633753`}, {1.597938144329897`, 0.044761696`}};

fit = NonlinearModelFit[Data, B/(
  1 + g (x - (1.42 + Ea))^(-3/2)), {B, g, Ea}, x]

which gives:

NonlinearModelFit::nrlnum: "The function value {-1.22471-0.217191\ I,-1.0682-0.243262\ I,-0.863406-0.265857\ I,-0.628591-0.289822\ I,<<12>>,0.26533 -0.472365\ I,0.318041 -0.47811\ I,0.312374 -0.479155\ I}\n is not a list of real numbers with dimensions {19} at {B,g,Ea} = {1.,1.,1.}."

The function I am using to fit my data gets imaginary values for some values of the parameters. But how can I force Mathematica to avoid these values?

share|improve this question
The reason is because it hit a negative value under the root, which ended up generating imaginary numbers. You can try using either assumptions, or use Abs, like this: !Mathematica graphics now it worked. If this meets your model or not, I do not know. I do not do stats. But that is the reason why it failed. – Nasser Aug 25 '13 at 5:05
another option is to add a constraint, like this !Mathematica graphics again, I do not know if this meets your model needs or not. – Nasser Aug 25 '13 at 5:16
When I try to evaluate the code, Mathematica 9.0.1 neither evaluates the code nor returns an error !Mathematica graphics. However following what @Nasser has suggested fixes the problem. – M6299 Aug 25 '13 at 5:31
@Nasser would you consider an answer? You solved the problem, so why not document it? – Yves Klett Aug 25 '13 at 6:42
This is a common problem. I've addressed it in my preferred fashion in this answer. – Oleksandr R. Aug 25 '13 at 15:37

I run a trace on the command, Trace[NonlinearModelFit[Data, B/(1 + g (x - (1.42 + Ea))^(-3/2)), {B, g, Ea}, x]] and looking at the result, I noticed a check is being done using FreeQ[...,Complex] and right after that, saw lots of $Failed messages (hard to read trace messages).

Mathematica graphics

So when I Saw that I realized it was the use of the root in the model. Internally, it was generating a numerical data to fit, and used values that caused a negative value to appear, for example

  B/(1 + g (x - (1.42 + Ea))^(-3/2)) /. {B -> 1, g -> 1, Ea -> 1,   x -> 1}
  (*  0.7411531317364896 - 0.4380013322510369 I  *)

And NonlinearModelFit does not like to work with complex numbers to make the fit.

So, what to do? Add a constraints, or use Abs value to make sure the value under the root remain non-negative. I also tried Assumptions, but these did not help.

The constraint is added after form. For example

NonlinearModelFit[Data, {B/(1 + g (x - (1.42 + Ea))^(-3/2)), Ea <= 0}, {B, g, Ea}, x]

Mathematica graphics

It seems your model did not consider that complex numbers can be generated for some values, and the correct constraint is needed to insure this does not happen.

share|improve this answer
Important to note is that specifying constraints also changes the method from Levenberg-Marquardt to NLIP. Although the latter will certainly obey any constraints given, its convergence properties do not seem to be as good. – Oleksandr R. Aug 25 '13 at 15:43

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