13.4. Fit Results and Outputs

Changed in version 0.9.34: minimize() returns a result group containing fit statistics.

After the fit has completed, several statistics are output and available to describe the quality of the fit and the estimated values for the Parameter values and uncertainties. The main statistics are written to group returned by minimize(), while the parameter values in paramgroup are updated to their best-fit values.

The estimated values, uncertainties, and correlations for each varied Parameter are written as attributes of that Parameter. Thus, after a fit, each variable Parameter par will be updated so that par.value will hold the estimated best-fit value, par.stderr will hold the estimated uncertainty (1-\(\sigma\) standard error), and par.correl will hold a dictionary of correlation values with the other variable Parameters.

General Fit statistics describing the quality of the fit and details about how the fit proceeded will be put into the result group with variable names and meanings as outlines in Table of Fit Statistics. For advanced users, the fitting class instance and result from lmfit are available.

Table of Fit Statistics and Results contained in the return value of minimize().

Listed are the names and description of items in the fit result group returned by the minimize() function. Many of these items are directly from lmfit.

name	Description of Statistical Quantity or Output
nvarys	number of variable parameters in the fit
ndata	number of data points
nfree	ndata - nfree
chi_square	chi-square: \(\chi^2 = \sum_i^N [{\rm Resid}_i]^2\)
chi_reduced	reduced chi-square: \(\chi^2_{\nu}= {\chi^2} / {(N - N_{\rm varys})}\) |
aic	Akaike Information Criteria
bic	Bayesian Information Criteria
residual	final residual array
covar	covariance matrix (ordered according to var_names).
var_names	list of variable parameter names
params	lmfit Parameters
fitter	lmfit Minimizer
fit_details	lmfit MinimizerResult
nfev	number of evaluations of the fit residual function.
success	bool (True or False) for whether fit appeared to succeed.
errorbars	bool (True or False) for whether uncertainties were estimated.
message	text message from fit
lmdif_message	text message from Fortran least-squares function

Changed in version 0.9.34: fit_report() uses a result group returned by minimize()

fit_report(result, show_correl=True, min_correl=0.1)

returns a fit report for a fit given a parameter group.

Parameters:

• result – fit result group, returned by minimize().

• show_correl – flag (True/False) to show parameter correlations.

• min_correl – smallest absolute value of correlation to show.

Returns:

string of fit report. This can be printed or stored.

A typical result from fit_report() would look like this:

larch> print fit_report(result)
[[Fit Statistics]]
    # function evals   = 28
    # data points      = 201
    # variables        = 4
    chi-square         = 0.50471
    reduced chi-square = 0.002562
    Akaike info crit   = -1195.4
    Bayesian info crit = -1182.2
[[Variables]]
    amp:   12.0312835 +/- 0.076725 (0.64%) (init= 5)
    wid:   2.01663402 +/- 0.011920 (0.59%) (init= 1)
    off:   0.99188155 +/- 0.005226 (0.53%) (init= 0)
    cen:   1.49995279 +/- 0.010144 (0.68%) (init= 2)
[[Correlations]] (unreported correlations are <  0.100)
    C(amp, off)                  = -0.730
    C(amp, wid)                  =  0.719
    C(wid, off)                  = -0.525