genmod.generalized_linear_model.GLM()

statsmodels.genmod.generalized_linear_model.GLM

class statsmodels.genmod.generalized_linear_model.GLM(endog, exog, family=None, offset=None, exposure=None, missing='none', **kwargs) [source]

Generalized Linear Models class

GLM inherits from statsmodels.base.model.LikelihoodModel

Parameters:

endog : array-like 1d array of endogenous response variable. This array can be 1d or 2d. Binomial family models accept a 2d array with two columns. If supplied, each observation is expected to be [success, failure]. exog : array-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 (models specified using a formula include an intercept by default). See statsmodels.tools.add_constant. family : family class instance The default is Gaussian. To specify the binomial distribution family = sm.family.Binomial() Each family can take a link instance as an argument. See statsmodels.family.family for more information. missing : str 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.?

See also

statsmodels.genmod.families.family, Families, Link Functions

Notes

Only the following combinations make sense for family and link

             + ident log logit probit cloglog pow opow nbinom loglog logc
Gaussian     |   x    x                        x
inv Gaussian |   x    x                        x
binomial     |   x    x    x     x       x     x    x           x      x
Poission     |   x    x                        x
neg binomial |   x    x                        x          x
gamma        |   x    x                        x

Not all of these link functions are currently available.

Endog and exog are references so that if the data they refer to are already arrays and these arrays are changed, endog and exog will change.

Attributes

df_model : float

Model degrees of freedom is equal to p - 1, where p is the number of regressors. Note that the intercept is not reported as a degree of freedom.

df_resid : float

Residual degrees of freedom is equal to the number of observation n minus the number of regressors p.

endog : array

See above. Note that endog is a reference to the data so that if data is already an array and it is changed, then endog changes as well.

exposure : array-like

Include ln(exposure) in model with coefficient constrained to 1. Can only be used if the link is the logarithm function.

exog : array

See above. Note that endog is a reference to the data so that if data is already an array and it is changed, then endog changes as well.

iteration : int

The number of iterations that fit has run. Initialized at 0.

family : family class instance

The distribution family of the model. Can be any family in statsmodels.families. Default is Gaussian.

mu : array

The mean response of the transformed variable. mu is the value of the inverse of the link function at lin_pred, where lin_pred is the linear predicted value of the WLS fit of the transformed variable. mu is only available after fit is called. See statsmodels.families.family.fitted of the distribution family for more information.

normalized_cov_params : array

The p x p normalized covariance of the design / exogenous data. This is approximately equal to (X.T X)^(-1)

offset : array-like

Include offset in model with coefficient constrained to 1.

pinv_wexog : array

The pseudoinverse of the design / exogenous data array. Note that GLM has no whiten method, so this is just the pseudo inverse of the design. The pseudoinverse is approximately equal to (X.T X)^(-1)X.T

scale : float

The estimate of the scale / dispersion of the model fit. Only available after fit is called. See GLM.fit and GLM.estimate_scale for more information.

scaletype : str

The scaling used for fitting the model. This is only available after fit is called. The default is None. See GLM.fit for more information.

weights : array

The value of the weights after the last iteration of fit. Only available after fit is called. See statsmodels.families.family for the specific distribution weighting functions.

Examples

>>> import statsmodels.api as sm
>>> data = sm.datasets.scotland.load()
>>> data.exog = sm.add_constant(data.exog)

Instantiate a gamma family model with the default link function.

>>> gamma_model = sm.GLM(data.endog, data.exog,
...                      family=sm.families.Gamma())

>>> gamma_results = gamma_model.fit()
>>> gamma_results.params
array([-0.01776527,  0.00004962,  0.00203442, -0.00007181,  0.00011185,
       -0.00000015, -0.00051868, -0.00000243])
>>> gamma_results.scale
0.0035842831734919055
>>> gamma_results.deviance
0.087388516416999198
>>> gamma_results.pearson_chi2
0.086022796163805704
>>> gamma_results.llf
-83.017202161073527

Attributes

df_model	float	p - 1, where p is the number of regressors including the intercept.
df_resid	float	The number of observation n minus the number of regressors p.
endog	array	See Parameters.
exog	array	See Parameters.
family	family class instance	A pointer to the distribution family of the model.
mu	array	The estimated mean response of the transformed variable.
normalized_cov_params	array	p x p normalized covariance of the design / exogenous data.
pinv_wexog	array	For GLM this is just the pseudo inverse of the original design.
scale	float	The estimate of the scale / dispersion. Available after fit is called.
scaletype	str	The scaling used for fitting the model. Available after fit is called.
weights	array	The value of the weights after the last iteration of fit.

Methods

estimate_scale(mu)	Estimates the dispersion/scale.
fit([start_params, maxiter, method, tol, ...])	Fits a generalized linear model for a given family.
fit_constrained(constraints[, start_params])	fit the model subject to linear equality constraints
from_formula(formula, data[, subset])	Create a Model from a formula and dataframe.
hessian(params[, scale, observed])	Hessian, second derivative of loglikelihood function
hessian_factor(params[, scale, observed])	Weights for calculating Hessian
information(params[, scale])	Fisher information matrix.
initialize()	Initialize a generalized linear model.
loglike(*args)	Loglikelihood function.
predict(params[, exog, exposure, offset, linear])	Return predicted values for a design matrix
score(params[, scale])	score, first derivative of the loglikelihood function
score_factor(params[, scale])	weights for score for each observation
score_obs(params[, scale])	score first derivative of the loglikelihood for each observation.
score_test(params_constrained[, ...])	score test for restrictions or for omitted variables

Attributes

endog_names
exog_names