# 12.4. 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