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Some experimental data was fitted, by using last squares, to a function $f_1(t;c_1)$, that depends parametrically on $c_1$ (that is, the best $c_1$ parameter, according to LS, was found by fitting).

I wish to fit the same data to another (but quite similar) function $f_2(t;c_2)$, but I do not have access to those data.

Intuitively I think that I can just sample $f_1(t;c_1)$ and fit $f_2(t;c_2)$ to those points.

My doubts are:

  • How confident can I be about $c_2$?
  • Is there a simple and better way?
  • What can I know about the $c_2$ obtained?
  • Is there some bias that can be estimated?

Any help is appreciated, even if it does not address all the points above

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    $\begingroup$ @Michael M, I know that the model fits very well the experimental data. Better that $f_2$. Also that the residues 'should' be relatively small, around 0.1-1% of the predicted values $\endgroup$ Commented Oct 11, 2017 at 20:17
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    $\begingroup$ @MartijnWeterings I think the OP means that $y_i=f_1(t_i;c:_1)$ had been already fitted by someone else, to data the OP has not access to. So s/he is asking how to fit $y_i=f_2(t_i;c:_2)$ to data s/he doesn't have. For this reason, s/he would like to simulate data from the fitted model. A parametric bootstrap of sorts... $\endgroup$
    – DeltaIV
    Commented Oct 12, 2017 at 9:18
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    $\begingroup$ In that case it wont work. Or at least, the interpretation should be limited. The proposed simulation of data is not a simulation of the data but instead a simulation of the function that has been fitted to the data (information from residuals is lost). With such a procedure one may answer whether f_2 is similar to f_1, and only indirectly (if f_1 is very similar to the data 0.1% - 1%) one may argue that the function f_2 is similar to the data as well. In this case.. I guess it is better not to speak about fitting f_2 to f_1 or data, but instead finding c_2 such that f_2 best approximates f_1. $\endgroup$ Commented Oct 12, 2017 at 9:42
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    $\begingroup$ @user1420303 people may prefer all they want, but it's a fact that you cannot say anything about how well $f_2$ fits data you don't have. Even the simulation approach I described (which assumes you have estimates for the SE of $c_1$ and the SE of residuals) makes numerous assumptions and cannot be considered a valid substitute for having the actual data. $\endgroup$
    – DeltaIV
    Commented Oct 13, 2017 at 21:41
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    $\begingroup$ @user1420303 to follow the procedure I suggested (which, I repeat, it's an hack, and most likely not valid), you need the fit statistics for $f_1$. Can you get them from the authors who fitted it? Even if they're not keen on sharing data, they might be ok with sharing fit stats, or they may have included them in some reports. The fact that $f_2$ and $f_1$ are so similar doesn't change the fact that $f_1$ was fitted to real data, and $f_2$ won't. On the contrary, if they're so similar, why don't you just use $f_1$? What kind of information do you expect to gain by fitting a similar... $\endgroup$
    – DeltaIV
    Commented Oct 14, 2017 at 10:13

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