statsmodels.discrete.discrete_model.Poisson.initialize Poisson.initialize() Initialize is called by statsmodels.model.LikelihoodModel.__init__ and should contain any preprocessing that needs to be done for a model.

statsmodels.discrete.discrete_model.Poisson.information Poisson.information(params) Fisher information matrix of model Returns -Hessian of loglike evaluated at params.

statsmodels.discrete.discrete_model.Poisson.hessian Poisson.hessian(params) [source] Poisson model Hessian matrix of the loglikelihood Parameters: params : array-like The parameters of the model Returns: hess : ndarray, (k_vars, k_vars) The Hessian, second derivative of loglikelihood function, evaluated at params Notes where the loglinear model is assumed

statsmodels.discrete.discrete_model.Poisson.from_formula classmethod Poisson.from_formula(formula, data, subset=None, *args, **kwargs) Create a Model from a formula and dataframe. Parameters: formula : str or generic Formula object The formula specifying the model data : array-like The data for the model. See Notes. subset : array-like An array-like object of booleans, integers, or index values that indicate the subset of df to use in the model. Assumes df is a pandas.DataFrame args :

statsmodels.discrete.discrete_model.Poisson.fit_regularized Poisson.fit_regularized(start_params=None, method='l1', maxiter='defined_by_method', full_output=1, disp=1, callback=None, alpha=0, trim_mode='auto', auto_trim_tol=0.01, size_trim_tol=0.0001, qc_tol=0.03, **kwargs) [source] Fit the model using a regularized maximum likelihood. The regularization method AND the solver used is determined by the argument method. Parameters: start_params : array-like, optional Initial guess of the sol

statsmodels.discrete.discrete_model.Poisson.fit_constrained Poisson.fit_constrained(constraints, start_params=None, **fit_kwds) [source] fit the model subject to linear equality constraints The constraints are of the form R params = q where R is the constraint_matrix and q is the vector of constraint_values. The estimation creates a new model with transformed design matrix, exog, and converts the results back to the original parameterization. Parameters: constraints : formula expression or

statsmodels.genmod.families.family.Poisson.fitted Poisson.fitted(lin_pred) Fitted values based on linear predictors lin_pred. Parameters: lin_pred : array Values of the linear predictor of the model. dot(X,beta) in a classical linear model. Returns: mu : array The mean response variables given by the inverse of the link function.

statsmodels.discrete.discrete_model.Poisson.fit Poisson.fit(start_params=None, method='newton', maxiter=35, full_output=1, disp=1, callback=None, **kwargs) [source] Fit the model using maximum likelihood. The rest of the docstring is from statsmodels.base.model.LikelihoodModel.fit Fit method for likelihood based models Parameters: start_params : array-like, optional Initial guess of the solution for the loglikelihood maximization. The default is an array of zeros. method : str, optional

statsmodels.genmod.families.family.Poisson.deviance Poisson.deviance(endog, mu, scale=1.0) [source] Poisson deviance function Parameters: endog : array-like Endogenous response variable mu : array-like Fitted mean response variable scale : float, optional An optional scale argument Returns: deviance : float The deviance function at (endog,mu) as defined below. Notes If a constant term is included it is defined as

statsmodels.discrete.discrete_model.Poisson.cov_params_func_l1 Poisson.cov_params_func_l1(likelihood_model, xopt, retvals) Computes cov_params on a reduced parameter space corresponding to the nonzero parameters resulting from the l1 regularized fit. Returns a full cov_params matrix, with entries corresponding to zero?d values set to np.nan.