pythonlinear-regressioncurve-fittingpower-law

How to perform a joint fit of several curves (in Python)?

Suppose I'm fitting some data points by a simple linear regression. Now I'd like to perform several joint linear regressions for several sets of data points. More specifically, I want one parameter to be equal among all fits, which is schematically depicted here for the y-axis intersection.

y-axis intersection

After searching Google for some time I could neither find any Python (Scipy) routine which does that, nor any general literature, how one would accomplish this.

Ideally, I want to perform those joint fits not only in the case of simple linear regressions, but also for more general fit functions (for instance, power-law fits with joint exponent).

Solution

  • The lmfit module allows you to do this, as mentioned in their FAQ:

    from lmfit import minimize, Parameters, fit_report
import numpy as np

# residual function to minimize
def fit_function(params, x=None, dat1=None, dat2=None):

    model1 = params['offset'] + x * params['slope1']
    model2 = params['offset'] + x * params['slope2']

    resid1 = dat1 - model1
    resid2 = dat2 - model2
    return np.concatenate((resid1, resid2))

# setup fit parameters
params = Parameters()
params.add('slope1', value=1)
params.add('slope2', value=-1)
params.add('offset', value=0.5)

# generate sample data
x = np.arange(0, 10)
slope1, slope2, offset = 1.1, -0.9, 0.2
y1 = slope1 * x + offset
y2 = slope2 * x + offset

# fit
out = minimize(residual, params, kws={"x": x, "dat1": y1, "dat2": y2})
print(fit_report(out))
# [[Fit Statistics]]
#     # fitting method   = leastsq
#     # function evals   = 9
#     # data points      = 20
#     # variables        = 3
#     chi-square         = 1.4945e-31
#     reduced chi-square = 8.7913e-33
#     Akaike info crit   = -1473.48128
#     Bayesian info crit = -1470.49408
# [[Variables]]
#     slope1:  1.10000000 +/- 8.2888e-18 (0.00%) (init = 1)
#     slope2: -0.90000000 +/- 8.2888e-18 (0.00%) (init = -1)
#     offset:  0.20000000 +/- 3.8968e-17 (0.00%) (init = 0.5)
# [[Correlations]] (unreported correlations are < 0.100)
#     C(slope1, offset) = -0.742
#     C(slope2, offset) = -0.742
#     C(slope1, slope2) =  0.551