[SciPy-User] Least Square fit and goodness of fit

Mon May 17 00:18:00 EDT 2010

On Sun, May 16, 2010 at 22:33, <josef.pktd at gmail.com> wrote:

> On Sun, May 16, 2010 at 9:05 PM, Benedikt Riedel <briedel at wisc.edu> wrote:
> > What I still do not understand is the fact that curve_fit gives me a
> > different output then leastsq, even though curve_fit calls leastsq.
> >
> > I tried to get the chi-squared because we want to plot contours of
> > chi-square from the minimum to the maximum. I used following code:
> >
> > fitfunc = lambda p,x: p[0]+ p[1]*exp(-x)
> > errfunc = lambda p, x, y: (y-fitfunc(p,x))
> > pinit = [20,20.]
> >
> > def func(x, a, b):
> >      return a*exp(-x) + b
> >
> > pfinal, covar = curve_fit(func,tau, R4ctsdataselect, p0=pinit,
> > sigma=R4errctsdataselect)
>
> this uses weighted least squares
> sigma : None or N-length sequence
>    If not None, it represents the standard-deviation of ydata. This
> vector, if given, will be used as weights in the least-squares problem
>
> In your initial example with leastsq you don't have any weighting,
> it's just ordinary least squares
>
> maybe that's the difference.
>
>
>
Yeah I guess that will be it.

>
> > print pfinal
> > print covar
> > dof=size(tau)-size(pinit)
> > print dof
> > chi2=(sum(pow(R4ctsdataselect-fitfunc(pinit, tau), 2)/fitfunc(pinit,
> > tau)))/dof
> > print chi2
> >
> > I am not 100% sure I am doing the degrees of freedom calculation right. I
> > got the chi-square formula from the Pearson chi-squared test.
>
> I don't recognize your formula for chi2, and I don't see the
> connection to Pearson chi-squared test .
>
> Do you have a reference?
>
>
I based my use of the Pearson test from what I read in an Econometrics book,
but wiki has the a pretty good description. I basically based it off the
example there. Where the expected would be what comes out of the fit and
what you is the "R4ctsdataselect" for those specific values.

http://en.wikipedia.org/wiki/Pearson%27s_chi-square_test

> Josef
>
>
Thanks again

Ben

>  >
> > Thank you very much for the help so far.
> >
> > Cheers,
> >
> > Ben
> >
> > On Sun, May 16, 2010 at 05:50, <josef.pktd at gmail.com> wrote:
> >>
> >> On Sun, May 16, 2010 at 12:12 AM, Benedikt Riedel <briedel at wisc.edu>
> >> wrote:
> >> >
> >> >
> >> > On Fri, May 14, 2010 at 14:51, <josef.pktd at gmail.com> wrote:
> >> >>
> >> >> On Fri, May 14, 2010 at 3:01 PM, Benedikt Riedel <briedel at wisc.edu>
> >> >> wrote:
> >> >> > Hey,
> >> >> >
> >> >> > I am fairly new Scipy and am trying to do a least square fit to a
> set
> >> >> > of
> >> >> > data. Currently, I am using following code:
> >> >> >
> >> >> > fitfunc = lambda p,x: p[0]+ p[1]*exp(-x)
> >> >> > errfunc = lambda p, x, y: (y-fitfunc(p,x))
> >> >> > pinit = [20,20.]
> >> >> > out = leastsq(errfunc, pinit, args=(tau,R4ctsdataselect),
> >> >> > full_output=1)
> >> >> >
> >> >> > I am now trying to get the goodness of fit out of this data. I am
> >> >> > sort
> >> >> > of
> >> >> > running into a brick wall because I found a lot of conflicting ways
> >> >> > of
> >> >> > how
> >> >> > to calculate it.
> >> >>
> >> >> For regression the usual is
> >> >> http://en.wikipedia.org/wiki/Coefficient_of_determination
> >> >> coefficient of determination is
> >> >>
> >> >>    R^2 = 1 - {SS_{err} / SS_{tot}}
> >> >>
> >> >> Note your fitfunc is linear in parameters and can be better estimated
> >> >> by linear least squares, OLS.
> >> >> linear regression is handled in statsmodels and you can get lot's of
> >> >> statistics without worrying about the formulas.
> >> >> If you only have one slope parameter, then scipy.stats.linregress
> also
> >> >> works
> >> >>
> >> >
> >> > Thanks for the information. I am still note quite sure if this is what
> >> > my
> >> > boss wants because there should not be an average y value.
> >>
> >> The definition of Rsquared is pretty uncontroversial with the y.mean()
> >> correction, if there is a constant in the regression (although I know
> >> mainly the linear case for this).
> >>
> >> If there is no constant in the regression, the definition or Rsquared
> >> is not clear/unambiguous, but usually used without mean correction of
> >> y.
> >>
> >> Josef
> >>
> >> >
> >> >>
> >> >> scipy.optimize.curve_fit (scipy 0.8) can also give you the covariance
> >> >> of the parameter estimates.
> >> >> http://docs.scipy.org/scipy/docs/scipy.optimize.minpack.curve_fit
> >> >
> >> > I have been trying this out, but the fit just looks horrid compared to
> >> > using
> >> > leastsq method even though they call the same function according to
> the
> >> > documentation.
> >> >
> >> >>
> >> >> > I am aware of the chisquare function in stats function, but the
> >> >> > documentation seems a little confusing to me. Any help would be
> >> >> > greatly
> >> >> > appreciates.
> >> >>
> >> >> chisquare and others like kolmogorov-smirnov are more for testing the
> >> >> goodness-of-fit of entire distributions, not for how well a curve or
> >> >> line fits the data.
> >> >>
> >> >
> >> > That is what I thought, which brought up my confusion when I asked
> other
> >> > people and they told me to use that
> >> >
> >> >>
> >> >> Josef
> >> >>
> >> >> >
> >> >> > Thanks very much in advance.
> >> >> >
> >> >> > Cheers,
> >> >> >
> >> >> > Ben
> >> >> >
> >> >> >
> >> >> >
> >> >> > _______________________________________________
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> >> >> > SciPy-User at scipy.org
> >> >> > http://mail.scipy.org/mailman/listinfo/scipy-user
> >> >> >
> >> >> >
> >> >> _______________________________________________
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> >> >
> >> >
> >> >
> >> > --
> >> > Benedikt Riedel
> >> > Graduate Student University of Wisconsin-Madison
> >> > Department of Physics
> >> > Office: 2304 Chamberlin Hall
> >> > Lab: 6247 Chamberlin Hall
> >> > Tel:  (608) 301-5736
> >> > Cell: (213) 519-1771
> >> > Lab: (608) 262-5916
> >> >
> >> > _______________________________________________
> >> > SciPy-User mailing list
> >> > SciPy-User at scipy.org
> >> > http://mail.scipy.org/mailman/listinfo/scipy-user
> >> >
> >> >
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> >
> >
> >
> > --
> > Benedikt Riedel
> > Graduate Student University of Wisconsin-Madison
> > Department of Physics
> > Office: 2304 Chamberlin Hall
> > Lab: 6247 Chamberlin Hall
> > Tel:  (608) 301-5736
> > Cell: (213) 519-1771
> > Lab: (608) 262-5916
> >
> > _______________________________________________
> > SciPy-User mailing list
> > SciPy-User at scipy.org
> > http://mail.scipy.org/mailman/listinfo/scipy-user
> >
> >
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-- 
Benedikt Riedel
Graduate Student University of Wisconsin-Madison
Department of Physics
Office: 2304 Chamberlin Hall
Lab: 6247 Chamberlin Hall
Tel:  (608) 301-5736
Cell: (213) 519-1771
Lab: (608) 262-5916
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