Chi-square value from lmfit

Question

I have been trying to do a pixel-to-pixel fitting of a set of images ie I have data at different wavelengths in different images and I am trying to fit a function for each pixel individually. I have done the fitting using lmfit and obtained the values of the unknown parameters for each pixel. Now, I want to obtain the chi-squared value for each fit. I know that lmfit has this attribute called chisqr which can give me the same but what is confusing me is this line from the lmfit github site: " Note that the calculation of chi-square and reduced chi-square assume that the returned residual function is scaled properly to the uncertainties in the data. For these statistics to be meaningful, the person writing the function to be minimized must scale them properly. " I doubt that the values I am getting from the chisqr attribute are not exactly right and some scaling needs to be done. Can somebody please explain how lmfit calculates the chisquare value and what scaling am I required to do?

This is a sample of my fitting function

def fcn2fit(params,freq,F,sigma):
    colden=params['colden'].value
    tk=params['tk'].value
    model = greybodyfit(np.array(freq),colden,tk)
    return (model - F)/sigma

colden and tk are the free parameters, freq is the independent variable and F is the dependent variable, sigma is the error in F. Is returning (model-F)/sigma the right way of scaling the residuals so that the chisqr attribute gives the correct chi-square value?

Answer 1

The value reported for chi-square is the sum of the square of the residual for the fit. Lmfit cannot tell whether that residual function is properly scaled by the standard error of the data - this scaling must be done in the objective function if you are using lmfit.minimize or passed in as weights if using lmfit.Model .