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.. currentmodule:: statsmodels.genmod.generalized_estimating_equations
.. _gee:
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', cache=True).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
^^^^^^^^^^^
.. autosummary::
:toctree: generated/
GEE
NominalGEE
OrdinalGEE
.. module:: statsmodels.genmod.qif
:synopsis: Quadratic inference functions
.. currentmodule:: statsmodels.genmod.qif
.. autosummary::
:toctree: generated/
QIF
Results Classes
^^^^^^^^^^^^^^^
.. currentmodule:: statsmodels.genmod.generalized_estimating_equations
.. autosummary::
:toctree: generated/
GEEResults
GEEMargins
.. currentmodule:: statsmodels.genmod.qif
.. autosummary::
:toctree: generated/
QIFResults
Dependence Structures
^^^^^^^^^^^^^^^^^^^^^
The dependence structures currently implemented are
.. module:: statsmodels.genmod.cov_struct
:synopsis: Covariance structures for Generalized Estimating Equations (GEE)
.. currentmodule:: statsmodels.genmod.cov_struct
.. autosummary::
:toctree: generated/
CovStruct
Autoregressive
Exchangeable
GlobalOddsRatio
Independence
Nested
Families
^^^^^^^^
The distribution families are the same as for GLM, currently implemented are
.. module:: statsmodels.genmod.families.family
:synopsis: Generalized Linear Model (GLM) families
.. currentmodule:: statsmodels.genmod.families.family
.. autosummary::
:toctree: generated/
Family
Binomial
Gamma
Gaussian
InverseGaussian
NegativeBinomial
Poisson
Tweedie
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
.. currentmodule:: statsmodels.genmod.families.links
.. autosummary::
:toctree: generated/
Link
CDFLink
CLogLog
Log
Logit
NegativeBinomial
Power
Cauchy
Identity
InversePower
InverseSquared
Probit
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