Quantifying the quality of curve fit using Python SciPy

Question

I’m using Scipy CurveFit to fit a Gaussian curve to data, and am interested in analysing the quality of the fit. I know CurveFit returns a useful pcov matrix, from which the standard deviation of each fitting parameter can be computed as sqrt(pcov[0,0]) for the parameter popt[0].

e.g. code snippet for this:

import numpy as np
from scipy.optimize import curve_fit

def gaussian(self, x, *p):
 A, sigma, mu, y_offset = p
return A*np.exp(-(x-mu)**2/(2.*sigma**2)) + y_offset

p0 = [1,2,3,4] #Initial guess of parameters
popt, pcov = curve_fit(gaussian, x,y, p0) #Return co-effs for fit and covariance

‘Parameter A is %f (%f uncertainty)’ % (popt[0], np.sqrt(pcov[0, 0]))

This gives an indication of the uncertainty in fitting parameters for each coefficient in the fitting curve equation, but I wonder how best to obtain an overall “quality of fit parameter” so that I can compare the quality of fit between different curve equations (e.g. Gaussian, Super Gaussian etc.)

On a simple level, I could just compute the percentage uncertainty in each coefficient and then average, although I wonder if there’s a better way? From searching online, and from the particularly useful “goodness of fit” Wikipedia page , I note there are many measures to describe this. I wonder if anyone knows whether any are built into Python packages / has any general advice for good ways to quantify curve fitting.

Thanks for any help!

Answer 1

You can use the ODRPACK library instead of the curve_fit. The result of fitting by the ODRPACK contains the estimates of uncertainties for all fitting parameters in several different ways including standard errors of the estimated parameters, which exactly you are looking for.

I used to work with the curve_fit, but I've faced the same problem: the absence of estimates of errors of fitting parameters. So, now I'm using the ODRPACK.