'Fit function for any model with an objective function.
Parameters
start_params : array-like, optional
Initial guess of the solution for the loglikelihood maximization.
The default is an array of zeros.
method : str {\'newton\',\'nm\',\'bfgs\',\'powell\',\'cg\',\'ncg\',\'basinhopping\',
\'minimize\'}
Method can be \'newton\' for Newton-Raphson, \'nm\' for Nelder-Mead,
\'bfgs\' for Broyden-Fletcher-Goldfarb-Shanno, \'powell\' for modified
Powell\'s method, \'cg\' for conjugate gradient, \'ncg\' for Newton-
conjugate gradient, \'basinhopping\' for global basin-hopping
solver, if available or a generic \'minimize\' which is a wrapper for
scipy.optimize.minimize. `method` determines which solver from
scipy.optimize is used. The explicit arguments in `fit` are passed
to the solver, with the exception of the basin-hopping solver. Each
solver has several optional arguments that are not the same across
solvers. See the notes section below (or scipy.optimize) for the
available arguments and for the list of explicit arguments that the
basin-hopping solver supports..
maxiter : int
The maximum number of iterations to perform.
full_output : bool
Set to True to have all available output in the Results object\'s
mle_retvals attribute. The output is dependent on the solver.
See LikelihoodModelResults notes section for more information.
disp : bool
Set to True to print convergence messages.
fargs : tuple
Extra arguments passed to the likelihood function, i.e.,
loglike(x,*args)
callback : callable callback(xk)
Called after each iteration, as callback(xk), where xk is the
current parameter vector.
retall : bool
Set to True to return list of solutions at each iteration.
Available in Results object\'s mle_retvals attribute.
Returns
xopt : array
The solution to the objective function
retvals : dict, None
If `full_output` is True then this is a dictionary which holds
information returned from the solver used. If it is False, this is
None.
optim_settings : dict
A dictionary that contains the parameters passed to the solver.
Notes
The \'basinhopping\' solver ignores `maxiter`, `retall`, `full_output`
explicit arguments.
Optional arguments for the solvers (available in Results.mle_settings)::
\'newton\'
tol : float
Relative error in params acceptable for convergence.
\'nm\' -- Nelder Mead
xtol : float
Relative error in params acceptable for convergence
ftol : float
Relative error in loglike(params) acceptable for
convergence
maxfun : int
Maximum number of function evaluations to make.
\'bfgs\'
gtol : float
Stop when norm of gradient is less than gtol.
norm : float
Order of norm (np.Inf is max, -np.Inf is min)
epsilon
If fprime is approximated, use this value for the step
size. Only relevant if LikelihoodModel.score is None.
\'cg\'
gtol : float
Stop when norm of gradient is less than gtol.
norm : float
Order of norm (np.Inf is max, -np.Inf is min)
epsilon : float
If fprime is approximated, use this value for the step
size. Can be scalar or vector.  Only relevant if
Likelihoodmodel.score is None.
\'ncg\'
fhess_p : callable f\'(x,*args)
Function which computes the Hessian of f times an arbitrary
vector, p.  Should only be supplied if
LikelihoodModel.hessian is None.
avextol : float
Stop when the average relative error in the minimizer
falls below this amount.
epsilon : float or ndarray
If fhess is approximated, use this value for the step size.
Only relevant if Likelihoodmodel.hessian is None.
\'powell\'
xtol : float
Line-search error tolerance
ftol : float
Relative error in loglike(params) for acceptable for
convergence.
maxfun : int
Maximum number of function evaluations to make.
start_direc : ndarray
Initial direction set.
\'basinhopping\'
niter : integer
The number of basin hopping iterations.
niter_success : integer
Stop the run if the global minimum candidate remains the
same for this number of iterations.
T : float
The "temperature" parameter for the accept or reject
criterion. Higher "temperatures" mean that larger jumps
in function value will be accepted. For best results
`T` should be comparable to the separation (in function
value) between local minima.
stepsize : float
Initial step size for use in the random displacement.
interval : integer
The interval for how often to update the `stepsize`.
minimizer : dict
Extra keyword arguments to be passed to the minimizer
`scipy.optimize.minimize()`, for example \'method\' - the
minimization method (e.g. \'L-BFGS-B\'), or \'tol\' - the
tolerance for termination. Other arguments are mapped from
explicit argument of `fit`:
- `args` <- `fargs`
- `jac` <- `score`
- `hess` <- `hess`
\'minimize\'
min_method : str, optional
Name of minimization method to use.
Any method specific arguments can be passed directly.
For a list of methods and their arguments, see
documentation of `scipy.optimize.minimize`.
If no method is specified, then BFGS is used.'

def _fit(self, objective, gradient, start_params, fargs, kwargs, hessian=None, method='newton', maxiter=100, full_output=True, disp=True, callback=None, retall=False):

    extra_fit_funcs = kwargs.setdefault('extra_fit_funcs', dict())
    methods = ['newton', 'nm', 'bfgs', 'lbfgs', 'powell', 'cg', 'ncg', 'basinhopping', 'minimize']
    methods += extra_fit_funcs.keys()
    method = method.lower()
    _check_method(method, methods)
    fit_funcs = {'newton': _fit_newton, 'nm': _fit_nm, 'bfgs': _fit_bfgs, 'lbfgs': _fit_lbfgs, 'cg': _fit_cg, 'ncg': _fit_ncg, 'powell': _fit_powell, 'basinhopping': _fit_basinhopping, 'minimize': _fit_minimize}
    if extra_fit_funcs:
        fit_funcs.update(extra_fit_funcs)
    func = fit_funcs[method]
    (xopt, retvals) = func(objective, gradient, start_params, fargs, kwargs, disp=disp, maxiter=maxiter, callback=callback, retall=retall, full_output=full_output, hess=hessian)
    optim_settings = {'optimizer': method, 'start_params': start_params, 'maxiter': maxiter, 'full_output': full_output, 'disp': disp, 'fargs': fargs, 'callback': callback, 'retall': retall}
    optim_settings.update(kwargs)
    return (xopt, retvals, optim_settings)
