Generalized Estimating Equations

Generalized Estimating Equations estimate generalized linear models for panel, cluster or repeated measures data when the observations are possibly correlated withing a cluster but uncorrelated across clusters. It supports estimation of the same one-parameter exponential families as Generalized Linear models (GLM).

See Module Reference_ for commands and arguments.

Examples

The following illustrates a Poisson regression with exchangeable correlation within clusters using data on epilepsy seizures.

.. ipython:: python

import statsmodels.api as sm
import statsmodels.formula.api as smf

data = sm.datasets.get_rdataset('epil', package='MASS').data

fam = sm.families.Poisson()
ind = sm.cov_struct.Exchangeable()
mod = smf.gee("y ~ age + trt + base", "subject", data,
              cov_struct=ind, family=fam)
res = mod.fit()
print(res.summary())

Several notebook examples of the use of GEE can be found on the Wiki: Wiki notebooks for GEE <https://github.com/statsmodels/statsmodels/wiki/Examples#generalized-estimating-equations-gee>_

References ^^^^^^^^^^

KY Liang and S Zeger. "Longitudinal data analysis using generalized linear models". Biometrika (1986) 73 (1): 13-22.
S Zeger and KY Liang. "Longitudinal Data Analysis for Discrete and Continuous Outcomes". Biometrics Vol. 42, No. 1 (Mar., 1986), pp. 121-130
A Rotnitzky and NP Jewell (1990). "Hypothesis testing of regression parameters in semiparametric generalized linear models for cluster correlated data", Biometrika, 77, 485-497.
Xu Guo and Wei Pan (2002). "Small sample performance of the score test in GEE". http://www.sph.umn.edu/faculty1/wp-content/uploads/2012/11/rr2002-013.pdf
LA Mancl LA, TA DeRouen (2001). A covariance estimator for GEE with improved small-sample properties. Biometrics. 2001 Mar;57(1):126-34.

Module Reference

.. module:: statsmodels.genmod.generalized_estimating_equations :synopsis: Generalized estimating equations

Model Class ^^^^^^^^^^^