statsmodels.discrete.discrete_model.NegativeBinomial

class statsmodels.discrete.discrete_model.NegativeBinomial(endog, exog, loglike_method='nb2', offset=None, exposure=None, missing='none', check_rank=True, **kwargs)

Negative Binomial Model

Parameters:

endogarray_like

A 1-d endogenous response variable. The dependent variable.

exogarray_like

A nobs x k array where nobs is the number of observations and k is the number of regressors. An intercept is not included by default and should be added by the user. See statsmodels.tools.add_constant.

loglike_methodstr

Log-likelihood type. ‘nb2’,’nb1’, or ‘geometric’. Fitted value \(\mu\) Heterogeneity parameter \(\alpha\)

• nb2: Variance equal to \(\mu + \alpha\mu^2\) (most common)

• nb1: Variance equal to \(\mu + \alpha\mu\)

• geometric: Variance equal to \(\mu + \mu^2\)

offsetarray_like

Offset is added to the linear prediction with coefficient equal to 1.

exposurearray_like

Log(exposure) is added to the linear prediction with coefficient equal to 1.

missingstr

Available options are ‘none’, ‘drop’, and ‘raise’. If ‘none’, no nan checking is done. If ‘drop’, any observations with nans are dropped. If ‘raise’, an error is raised. Default is ‘none’.

check_rankbool

Check exog rank to determine model degrees of freedom. Default is True. Setting to False reduces model initialization time when exog.shape[1] is large.

Attributes:

endogndarray

A reference to the endogenous response variable

exogndarray

A reference to the exogenous design.

Methods

cdf(X)	The cumulative distribution function of the model.
cov_params_func_l1(likelihood_model, xopt, ...)	Computes cov_params on a reduced parameter space corresponding to the nonzero parameters resulting from the l1 regularized fit.
fit([start_params, method, maxiter, ...])	Fit the model using maximum likelihood.
fit_regularized([start_params, method, ...])	Fit the model using a regularized maximum likelihood.
from_formula(formula, data[, subset, drop_cols])	Create a Model from a formula and dataframe
get_distribution(params[, exog, exposure, ...])	Get a frozen instance of distribution Get frozen instance of distribution based on predicted parameters
hessian(params)	The Hessian matrix of the model
information(params)	Fisher information matrix of model
initialize()	Initialize is called by statsmodels.model.LikelihoodModel.__init__ and should contain any preprocessing that needs to be done for a model.
loglike(params)	Log-likelihood for negative binomial model.
pdf(X)	The probability density (mass) function of the model.
predict(params[, exog, exposure, offset, ...])	Predict response variable of a model given exogenous variables.
score(params)	Score vector of model
score_obs(params)

References

Greene, W. 2008. “Functional forms for the negative binomial model

for count data”. Economics Letters. Volume 99, Number 3, pp.585-590.

Hilbe, J.M. 2011. “Negative binomial regression”. Cambridge University

Press.

Methods

cdf(X)	The cumulative distribution function of the model.
cov_params_func_l1(likelihood_model, xopt, ...)	Computes cov_params on a reduced parameter space corresponding to the nonzero parameters resulting from the l1 regularized fit.
fit([start_params, method, maxiter, ...])	Fit the model using maximum likelihood.
fit_regularized([start_params, method, ...])	Fit the model using a regularized maximum likelihood.
from_formula(formula, data[, subset, drop_cols])	Create a Model from a formula and dataframe
get_distribution(params[, exog, exposure, ...])	Get a frozen instance of distribution Get frozen instance of distribution based on predicted parameters
hessian(params)	The Hessian matrix of the model
information(params)	Fisher information matrix of model
initialize()	Initialize is called by statsmodels.model.LikelihoodModel.__init__ and should contain any preprocessing that needs to be done for a model.
loglike(params)	Log-likelihood for negative binomial model.
pdf(X)	The probability density (mass) function of the model.
predict(params[, exog, exposure, offset, ...])	Predict response variable of a model given exogenous variables.
score(params)	Score vector of model
score_obs(params)

Properties

endog_names	Names of endogenous variables
exog_names	Names of exogenous variables