statsmodels.genmod.generalized_estimating_equations.GEE

class statsmodels.genmod.generalized_estimating_equations.GEE(endog, exog, groups, time=None, family=None, cov_struct=None, missing='none', offset=None, exposure=None, dep_data=None, constraint=None, update_dep=True, weights=None, **kwargs)[source]

Estimation of marginal regression models using Generalized Estimating Equations (GEE).

Marginal regression model fit using Generalized Estimating Equations.

GEE can be used to fit Generalized Linear Models (GLMs) when the data have a grouped structure, and the observations are possibly correlated within groups but not between groups.

Parameters:
  • endog (array-like) – 1d array of endogenous values (i.e. responses, outcomes, dependent variables, or ‘Y’ values).
  • exog (array-like) – 2d array of exogeneous values (i.e. covariates, predictors, independent variables, regressors, or ‘X’ values). 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.
  • groups (array-like) – A 1d array of length nobs containing the group labels.
  • time (array-like) – A 2d array of time (or other index) values, used by some dependence structures to define similarity relationships among observations within a cluster.
  • family (family class instance) – The default is Gaussian. To specify the binomial distribution use family=sm.families.Binomial(). Each family can take a link instance as an argument. See statsmodels.genmod.families.family for more information.
  • cov_struct (CovStruct class instance) – The default is Independence. To specify an exchangeable structure use cov_struct = Exchangeable(). See statsmodels.genmod.cov_struct.CovStruct for more information.
  • offset (array-like) – An offset to be included in the fit. If provided, must be an array whose length is the number of rows in exog.
  • dep_data (array-like) – Additional data passed to the dependence structure.
  • constraint ((ndarray, ndarray)) – If provided, the constraint is a tuple (L, R) such that the model parameters are estimated under the constraint L * param = R, where L is a q x p matrix and R is a q-dimensional vector. If constraint is provided, a score test is performed to compare the constrained model to the unconstrained model.
  • update_dep (bool) – If true, the dependence parameters are optimized, otherwise they are held fixed at their starting values.
  • weights (array-like) – An array of weights to use in the analysis. The weights must be constant within each group. These correspond to probability weights (pweights) in Stata.
  • 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.

The “robust” covariance type is the standard “sandwich estimator” (e.g. Liang and Zeger (1986)). It is the default here and in most other packages. The “naive” estimator gives smaller standard errors, but is only correct if the working correlation structure is correctly specified. The “bias reduced” estimator of Mancl and DeRouen (Biometrics, 2001) reduces the downard bias of the robust estimator.

The robust covariance provided here follows Liang and Zeger (1986) and agrees with R’s gee implementation. To obtain the robust standard errors reported in Stata, multiply by sqrt(N / (N - g)), where N is the total sample size, and g is the average group size.

Examples

Logistic regression with autoregressive working dependence:

>>> import statsmodels.api as sm
>>> family = sm.families.Binomial()
>>> va = sm.cov_struct.Autoregressive()
>>> model = sm.GEE(endog, exog, group, family=family, cov_struct=va)
>>> result = model.fit()
>>> print(result.summary())

Use formulas to fit a Poisson GLM with independent working dependence:

>>> import statsmodels.api as sm
>>> fam = sm.families.Poisson()
>>> ind = sm.cov_struct.Independence()
>>> model = sm.GEE.from_formula("y ~ age + trt + base", "subject",                                  data, cov_struct=ind, family=fam)
>>> result = model.fit()
>>> print(result.summary())

Equivalent, using the formula API:

>>> import statsmodels.api as sm
>>> import statsmodels.formula.api as smf
>>> fam = sm.families.Poisson()
>>> ind = sm.cov_struct.Independence()
>>> model = smf.gee("y ~ age + trt + base", "subject",                     data, cov_struct=ind, family=fam)
>>> result = model.fit()
>>> print(result.summary())

Methods

cluster_list(array) Returns array split into subarrays corresponding to the cluster structure.
estimate_scale() Returns an estimate of the scale parameter at the current parameter value.
fit([maxiter, ctol, start_params, …]) Fits a marginal regression model using generalized estimating equations (GEE).
from_formula(formula, groups, data[, …]) Create a Model from a formula and dataframe.
mean_deriv(exog, lin_pred) Derivative of the expected endog with respect to the parameters.
mean_deriv_exog(exog, params[, offset_exposure]) Derivative of the expected endog with respect to exog.
predict(params[, exog, offset, exposure, linear]) Return predicted values for a marginal regression model fit using GEE.
update_cached_means(mean_params) cached_means should always contain the most recent calculation of the group-wise mean vectors.

Attributes

cached_means
endog_names Names of endogenous variables
exog_names Names of exogenous variables