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

Ordinal Response Marginal Regression Model using 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.


1d array of endogenous values (i.e. responses, outcomes, dependent variables, or ‘Y’ values).


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


A 1d array of length nobs containing the group labels.


A 2d array of time (or other index) values, used by some dependence structures to define similarity relationships among observations within a cluster.

familyfamily class instance

The only family supported is Binomial. The default Logit link may be replaced with probit if desired.

cov_structCovStruct class instance

The default is Independence. To specify an exchangeable structure use cov_struct = Exchangeable(). See statsmodels.genmod.cov_struct.CovStruct for more information.


An offset to be included in the fit. If provided, must be an array whose length is the number of rows in exog.


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.


If true, the dependence parameters are optimized, otherwise they are held fixed at their starting values.


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.


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’.


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
Poisson     |   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 downward 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.


Fit an ordinal regression model using GEE, with “global odds ratio” dependence:

>>> import statsmodels.api as sm
>>> gor = sm.cov_struct.GlobalOddsRatio("ordinal")
>>> model = sm.OrdinalGEE(endog, exog, groups, cov_struct=gor)
>>> result =
>>> print(result.summary())

Using formulas:

>>> import statsmodels.formula.api as smf
>>> model = smf.ordinal_gee("y ~ x1 + x2", groups, data,
>>> result =
>>> print(result.summary())



Returns array split into subarrays corresponding to the cluster structure.


Perform a score test for the given submodel against this model.


Estimate the dispersion/scale.

fit([maxiter, ctol, start_params, …])

Fits a marginal regression model using generalized estimating equations (GEE).

fit_regularized(pen_wt[, scad_param, …])

Regularized estimation for 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.

qic(params, scale, cov_params)

Returns quasi-information criteria and quasi-likelihood values.

setup_ordinal(endog, exog, groups, time, offset)

Restructure ordinal data as binary indicators so that they can be analyzed using Generalized Estimating Equations.


cached_means should always contain the most recent calculation of the group-wise mean vectors.




Names of endogenous variables.


Names of exogenous variables.