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)[source]

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.

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.

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.

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)

Loglikelihood for negative binomial model

pdf(X)

The probability density (mass) function of the model.

predict(params[, exog, exposure, offset, linear])

Predict response variable of a count 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.