Generalized Estimating Equations

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.

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

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

Model Class

Results Classes

Dependence Structures

The dependence structures currently implemented are

Families

The distribution families are the same as for GLM, currently implemented are

Link Functions

The link functions are the same as for GLM, currently implemented are the following. Not all link functions are available for each distribution family. The list of available link functions can be obtained by

>>> sm.families.family.<familyname>.links