Fit the model using maximum likelihood.
The rest of the docstring is from statsmodels.base.model.LikelihoodModel.fit
Fit method for likelihood based models
Initial guess of the solution for the loglikelihood maximization. The default is an array of zeros.
The method determines which solver from scipy.optimize is used, and it can be chosen from among the following strings:
‘newton’ for Newton-Raphson, ‘nm’ for Nelder-Mead
‘bfgs’ for Broyden-Fletcher-Goldfarb-Shanno (BFGS)
‘lbfgs’ for limited-memory BFGS with optional box constraints
‘powell’ for modified Powell’s method
‘cg’ for conjugate gradient
‘ncg’ for Newton-conjugate gradient
‘basinhopping’ for global basin-hopping solver
‘minimize’ for generic wrapper of scipy minimize (BFGS by default)
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.
The maximum number of iterations to perform.
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.
Set to True to print convergence messages.
Extra arguments passed to the likelihood function, i.e., loglike(x,*args)
Called after each iteration, as callback(xk), where xk is the current parameter vector.
Set to True to return list of solutions at each iteration. Available in Results object’s mle_retvals attribute.
If False (default), then the negative inverse hessian is calculated after the optimization. If True, then the hessian will not be calculated. However, it will be available in methods that use the hessian in the optimization (currently only with “newton”).
All kwargs are passed to the chosen solver with one exception. The following keyword controls what happens after the fit:
warn_convergence : bool, optional If True, checks the model for the converged flag. If the converged flag is False, a ConvergenceWarning is issued.
The ‘basinhopping’ solver ignores maxiter, retall, full_output explicit arguments.
Optional arguments for solvers (see returned 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. 'lbfgs' m : int This many terms are used for the Hessian approximation. factr : float A stop condition that is a variant of relative error. pgtol : float A stop condition that uses the projected gradient. epsilon If fprime is approximated, use this value for the step size. Only relevant if LikelihoodModel.score is None. maxfun : int Maximum number of function evaluations to make. bounds : sequence (min, max) pairs for each element in x, defining the bounds on that parameter. Use None for one of min or max when there is no bound in that direction. '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 : int The number of basin hopping iterations. niter_success : int 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 : int 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.