0
$\begingroup$

I fitting an expression of the form:

$s(t)=\frac{1}{1+\exp[a+\sum_k b_k x_k(t)]}$

Where $a$ and $b_k$ are fitting parameters and $x_k(t)$ an input time series. I have $k=1,...,N$ different types of input variables and I'm trying to find what is the combination among the $N$ time series that best fit the observed data.

If I only use the first $k=1$ time series I have a better fitting result (better RMS), that if I use $k=1$ and $k=2$ together. So, my question is: why does the fitting Method (NMinimize of NonlinearModelFit function from Mathematica 10), when $x_1$ and $x_2$ are included at the same time, does not find the $b_1$ solution equal to the fitting process where only $x_1$ is present, together with $b_2=0.0$ result?

Improve this question
$\endgroup$
2
  • 1
    $\begingroup$ because the $a$ parameter is shared between the two groups, so fitting to both groups requires a compromise between the best-fitting values for the two groups ... ? $\endgroup$
    – Ben Bolker
    Commented Sep 7, 2015 at 15:45
  • $\begingroup$ Because a better fit is possible if the estimate, $b_2$, is allowed to move from being forced to be 0. (NB it's best to have your notation distinguish your estimates from the thing they're estimating.) $\endgroup$
    – Glen_b
    Commented Sep 7, 2015 at 22:46

0

Reset to default

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Browse other questions tagged or ask your own question.